Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
186 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C11 |
| prime radical | C11×#127 | C22 |
| 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×#500 | C2 | semidirect |
| 3. C11×#487 | C2 | semidirect |
| 4. C11×#487 | C2 | semidirect |
| 7. C11×#322 | C2 | semidirect |
| 38. #1719 | C11 | direct (N × H) |
| 55. #500 | C2×C11 | semidirect |
| 57. #487 | C2×C11 | semidirect |
| 58. #487 | C2×C11 | semidirect |
| 61. #322 | C2×C11 | semidirect |
| 106. C11 | #1719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#500 | 2 |
| C11×#492 | 2 |
| C11×#487 | 2 |
| C11×#486 | 2 |
| C11×#322 | 2 |
| #1719 | 11 |