Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
644 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#381 | C2 |
| hypercenter | #381 | D11 |
| hypocenter | C11 | #2815 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66983 | C2 | semidirect |
| 2. C11×#381 | C2 | semidirect |
| 3. #10622573 | C2 | semidirect |
| 4. #10622287 | C2 | semidirect |
| 5. #10622284 | C2 | semidirect |
| 20. C22×C4×C11 | D4 | semidirect |
| 58. #381 | D11 | semidirect |
| 99. C22×C4 | D44 | semidirect |
| 106. C11 | #2815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66983 | 2 |
| C11×#381 | 2 |
| #10622573 | 2 |
| #10622287 | 2 |
| #10622284 | 2 |
| #2815 | 11 |