Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
760 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C2×C23×H(5,𝔽2) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#137 | C2 | semidirect |
| 3. C2×C23×#124 | C2 | semidirect |
| 4. C23×#455 | C2 | direct (N × H) |
| 5. C2×C23×#104 | C2 | semidirect |
| 6. C2×C23×#100 | C2 | semidirect |
| 12. C22×Q8×C23 | C22 | semidirect |
| 17. C23×#137 | C22 | semidirect |
| 20. C2×M16×C23 | C22 | semidirect |
| 22. C23×#124 | C22 | semidirect |
| 24. C2×C42×C23 | C22 | semidirect |
| 25. C23×#104 | C22 | semidirect |
| 26. C23×#100 | C22 | semidirect |
| 39. C2×Q8×C23 | C23 | semidirect |
| 59. M16×C23 | C23 | semidirect |
| 63. C42×C23 | C23 | semidirect |
| 97. C2×#455 | C23 | direct (N × H) |
| 115. C2×#137 | C2×C23 | semidirect |
| 116. C2×#124 | C2×C23 | semidirect |
| 117. #455 | C2×C23 | direct (N × H) |
| 118. C2×#104 | C2×C23 | semidirect |
| 119. C2×#100 | C2×C23 | semidirect |
| 124. C2×C23 | #455 | direct (N × H) |
| 131. C22×Q8 | C22×C23 | semidirect |
| 136. #137 | C22×C23 | semidirect |
| 139. C2×M16 | C22×C23 | semidirect |
| 141. #124 | C22×C23 | semidirect |
| 143. C2×C42 | C22×C23 | semidirect |
| 144. #104 | C22×C23 | semidirect |
| 145. #100 | C22×C23 | semidirect |
| 146. C23 | C2×#455 | direct (N × H) |
| 159. C2×Q8 | C23×C23 | semidirect |
| 179. M16 | C23×C23 | semidirect |
| 183. C42 | C23×C23 | semidirect |
| 237. C2 | C23×#455 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×H(5,𝔽2) | 2 |
| C2×C23×#137 | 2 |
| C2×C23×#124 | 2 |
| C23×#455 | 2 |
| C2×C23×#104 | 2 |
| C2×C23×#100 | 2 |
| C2×#455 | 23 |