Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C2×C11×#117 | C2 |
| hypercenter | C2×#117 | D11 |
| hypocenter | C11 | #2619 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#117 | C2 | semidirect |
| 2. C2×#66983 | C2 | semidirect |
| 3. C2×#66927 | C2 | semidirect |
| 4. #10622604 | C2 | semidirect |
| 5. #10622573 | C2 | semidirect |
| 6. #10622552 | C2 | semidirect |
| 7. #10622549 | C2 | semidirect |
| 27. C22×C4×C11 | D4 | semidirect |
| 43. C42×C11 | D4 | semidirect |
| 76. C2×#117 | D11 | semidirect |
| 132. C22×C4 | D44 | semidirect |
| 143. C42 | C22⋊D11 | semidirect |
| 144. C11 | #2619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#117 | 2 |
| C2×#66983 | 2 |
| C2×#66927 | 2 |
| #10622604 | 2 |
| #10622573 | 2 |
| #10622552 | 2 |
| #10622549 | 2 |
| #2619 | 11 |