Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. C4⋊C4×D431 | C2 | semidirect |
| 3. #28352120 | C2 | semidirect |
| 4. #28352111 | C2 | semidirect |
| 5. #28352109 | C2 | semidirect |
| 6. (C2×D431)⋊C8 | C2 | semidirect |
| 7. #106×C431 | C2 | semidirect |
| 52. C431 | #481 | semidirect |
| 57. #106 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352164 | 2 |
| C4⋊C4×D431 | 2 |
| #28352120 | 2 |
| #28352111 | 2 |
| #28352109 | 2 |
| (C2×D431)⋊C8 | 2 |
| #106×C431 | 2 |
| #481 | 431 |