Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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×#384 | C2 |
| prime radical | C22×D44 | C22 |
| hypercenter | #384 | D11 |
| hypocenter | C11 | #2542 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66949 | C2 | semidirect |
| 3. C2×#66941 | C2 | semidirect |
| 4. C11×#384 | C2 | semidirect |
| 5. #10622605 | C2 | semidirect |
| 7. #10622589 | C2 | semidirect |
| 9. C4×Dic11⋊C4 | C2 | semidirect |
| 41. C2×D44 | Q8 | semidirect |
| 56. Dic11⋊C4 | D4 | semidirect |
| 95. #384 | D11 | semidirect |
| 110. C4×C11 | C22⋊Q8 | semidirect |
| 170. C11 | #2542 | semidirect |
| 216. C4 | #66949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66949 | 2 |
| C2×#66946 | 2 |
| C2×#66941 | 2 |
| C11×#384 | 2 |
| #10622605 | 2 |
| #10622601 | 2 |
| #10622589 | 2 |
| #10622552 | 2 |
| C4×Dic11⋊C4 | 2 |
| #2542 | 11 |