Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
452 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C24 |
| commutator | C22 | C23×C4×C23 |
| Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C22×C23 | C23×C4 |
| prime radical | C22×D4×C23 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#436 | C2 | semidirect |
| 3. C23×#431 | C2 | semidirect |
| 4. C23×#407 | C2 | semidirect |
| 7. C2×M16×C23 | C22 | semidirect |
| 13. C23×C4⋊C8 | C22 | semidirect |
| 15. C23×C22⋊C8 | C22 | semidirect |
| 16. C4×C8×C23 | C22 | semidirect |
| 44. C2×C4×C23 | M16 | semidirect |
| 51. #2975 | C23 | direct (N × H) |
| 66. #436 | C2×C23 | semidirect |
| 67. #431 | C2×C23 | semidirect |
| 68. #407 | C2×C23 | semidirect |
| 76. C2×M16 | C22×C23 | semidirect |
| 82. C4⋊C8 | C22×C23 | semidirect |
| 84. C22⋊C8 | C22×C23 | semidirect |
| 85. C4×C8 | C22×C23 | semidirect |
| 86. C23 | #2975 | direct (N × H) |
| 114. C2×C4 | M16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C23 | 2 |
| C23×#436 | 2 |
| C23×#431 | 2 |
| C23×#407 | 2 |
| #2975 | 23 |