Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
346 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #386 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#518 | C2 | semidirect |
| 3. C23×#421 | C2 | semidirect |
| 4. C23×#418 | C2 | semidirect |
| 5. C23×#410 | C2 | semidirect |
| 6. C23×#344 | C2 | semidirect |
| 7. C23×H(3,ℤ/4) | C2 | semidirect |
| 12. C2×SD16×C23 | C4 | semidirect |
| 13. C2×D8×C23 | C4 | semidirect |
| 30. C2×Q8×C23 | C2×C4 | semidirect |
| 36. C2×D4×C23 | C2×C4 | semidirect |
| 49. C2×C8×C23 | C2×C4 | semidirect |
| 91. #1904 | C23 | direct (N × H) |
| 111. #518 | C2×C23 | semidirect |
| 112. #421 | C2×C23 | semidirect |
| 113. #418 | C2×C23 | semidirect |
| 114. #410 | C2×C23 | semidirect |
| 115. #344 | C2×C23 | semidirect |
| 116. H(3,ℤ/4) | C2×C23 | semidirect |
| 127. C2×SD16 | C4×C23 | semidirect |
| 128. C2×D8 | C4×C23 | semidirect |
| 140. C23 | #1904 | direct (N × H) |
| 146. C2×Q8 | C2×C4×C23 | semidirect |
| 152. C2×D4 | C2×C4×C23 | semidirect |
| 165. C2×C8 | C2×C4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×AGL(1,ℤ/8) | 2 |
| C23×#518 | 2 |
| C23×#421 | 2 |
| C23×#418 | 2 |
| C23×#410 | 2 |
| C23×#344 | 2 |
| C23×H(3,ℤ/4) | 2 |
| #1904 | 23 |