Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #28352188 | C2 | semidirect |
| 2. #28352187 | C2 | semidirect |
| 3. #28352179 | C2 | semidirect |
| 7. C4×Dic862 | C2 | semidirect |
| 8. C4×Dic862 | C2 | semidirect |
| 11. C4×Q8×C431 | C2 | semidirect |
| 45. C4×D431 | Q8 | semidirect |
| 70. C431 | #533 | semidirect |
| 80. C4×Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352188 | 2 |
| #28352187 | 2 |
| #28352179 | 2 |
| #28352169 | 2 |
| #28352167 | 2 |
| #28352165 | 2 |
| C4×Dic862 | 2 |
| #28352146 | 2 |
| C42×D431 | 2 |
| C4×Q8×C431 | 2 |
| #533 | 431 |