Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
924 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
| hypercenter | #384 | D11 |
| hypocenter | C11 | #2856 |
| 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×#66948 | C2 | semidirect |
| 2. C2×#66927 | C2 | semidirect |
| 3. C2×C42×D11 | C2 | semidirect |
| 4. C11×#384 | C2 | semidirect |
| 5. #10622601 | C2 | semidirect |
| 27. C2×C4×D11 | D4 | semidirect |
| 29. C42×C11 | D4 | semidirect |
| 54. #384 | D11 | semidirect |
| 63. C2×D11 | #127 | semidirect |
| 65. C4×C11 | #121 | semidirect |
| 97. C42 | D44 | semidirect |
| 98. C11 | #2856 | semidirect |
| 127. C4 | #66948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66948 | 2 |
| C2×#66927 | 2 |
| C2×C42×D11 | 2 |
| C11×#384 | 2 |
| #10622601 | 2 |
| #2856 | 11 |