Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
200 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C11 |
| 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 |
|---|---|---|
| 48. #1645 | C11 | direct (N × H) |
| 56. Q8×C11 | Q16 | semidirect |
| 131. C11 | #1645 | direct (N × H) |
| 139. Q8 | C11×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C11 | 2 |
| C11×#487 | 2 |
| C11×#475 | 2 |
| C11×#462 | 2 |
| C11×#333 | 2 |
| C11×Q8⋊C8 | 2 |
| #1645 | 11 |