Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20293784 | C2 | semidirect |
| 2. C2×C8×D431 | C2 | semidirect |
| 4. Dic431⋊C8 | C2 | semidirect |
| 5. (C2×D431)⋊C8 | C2 | semidirect |
| 6. #28352099 | C2 | semidirect |
| 7. C22⋊C8×C431 | C2 | semidirect |
| 29. C431⋊C8 | D4 | semidirect |
| 43. C2×D431 | M16 | semidirect |
| 55. C431 | #435 | semidirect |
| 62. C22⋊C8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293784 | 2 |
| C2×C8×D431 | 2 |
| C4×C22⋊D431 | 2 |
| Dic431⋊C8 | 2 |
| (C2×D431)⋊C8 | 2 |
| #28352099 | 2 |
| C22⋊C8×C431 | 2 |
| #435 | 431 |