Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
520 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| prime radical | C11×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#401 | C2 | semidirect |
| 2. C11×#393 | C2 | semidirect |
| 4. C11×#386 | C2 | semidirect |
| 5. C11×#381 | C2 | semidirect |
| 30. #2760 | C11 | direct (N × H) |
| 47. #401 | C2×C11 | semidirect |
| 48. #393 | C2×C11 | semidirect |
| 50. #386 | C2×C11 | semidirect |
| 51. #381 | C2×C11 | semidirect |
| 92. C11 | #2760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#401 | 2 |
| C11×#393 | 2 |
| C11×#392 | 2 |
| C11×#386 | 2 |
| C11×#381 | 2 |
| #2760 | 11 |