Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 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 | C23 | C22×C4×C23 |
| Frattini, cosocle | C24 | C23×C23 |
| prime radical | C23×#534 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C24×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#518 | C2 | semidirect |
| 3. C2×C23×#99 | C2 | semidirect |
| 4. C2×C23×#99 | C2 | semidirect |
| 5. C23×#342 | C2 | semidirect |
| 9. C23×#123 | C4 | semidirect |
| 12. C23×#120 | C4 | semidirect |
| 21. C24×C23 | C2×C4 | semidirect |
| 37. C22×C4×C23 | C2×C4 | semidirect |
| 48. C22⋊C4×C23 | C2×C4 | semidirect |
| 49. C22⋊C4×C23 | D4 | semidirect |
| 82. #1913 | C23 | direct (N × H) |
| 106. #518 | C2×C23 | semidirect |
| 107. C2×#99 | C2×C23 | semidirect |
| 108. C2×#99 | C2×C23 | semidirect |
| 109. #342 | C2×C23 | semidirect |
| 121. #123 | C4×C23 | semidirect |
| 124. #120 | C4×C23 | semidirect |
| 133. C23 | #1913 | direct (N × H) |
| 134. C24 | C2×C4×C23 | semidirect |
| 150. C22×C4 | C2×C4×C23 | semidirect |
| 161. C22⋊C4 | C2×C4×C23 | semidirect |
| 162. C22⋊C4 | D4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#534 | 2 |
| C23×#518 | 2 |
| C2×C23×#99 | 2 |
| C23×#342 | 2 |
| #1913 | 23 |