Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C11 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C11 |
| prime radical | C11×#459 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#486 | C2 | semidirect |
| 2. C11×#461 | C2 | semidirect |
| 4. C11×#436 | C2 | semidirect |
| 5. C11×#334 | C2 | semidirect |
| 6. C11×#332 | C2 | semidirect |
| 7. C11×#331 | C2 | semidirect |
| 42. #1701 | C11 | direct (N × H) |
| 66. #486 | C2×C11 | semidirect |
| 67. #461 | C2×C11 | semidirect |
| 69. #436 | C2×C11 | semidirect |
| 70. #334 | C2×C11 | semidirect |
| 71. #332 | C2×C11 | semidirect |
| 72. #331 | C2×C11 | semidirect |
| 126. C11 | #1701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#486 | 2 |
| C11×#461 | 2 |
| C11×#459 | 2 |
| C11×#436 | 2 |
| C11×#334 | 2 |
| C11×#332 | 2 |
| C11×#331 | 2 |
| #1701 | 11 |