Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C11 |
| prime radical | C22×D4×C11 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#106 | C2 | semidirect |
| 4. C11×#384 | C2 | semidirect |
| 5. C11×#336 | C2 | semidirect |
| 33. #2094 | C11 | direct (N × H) |
| 54. C2×#106 | C2×C11 | semidirect |
| 57. #384 | C2×C11 | semidirect |
| 58. #336 | C2×C11 | semidirect |
| 107. C11 | #2094 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#106 | 2 |
| C2×C11×#102 | 2 |
| C11×#390 | 2 |
| C11×#384 | 2 |
| C11×#336 | 2 |
| #2094 | 11 |