Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22582926 | C2 | semidirect |
| 2. #22582909 | C2 | semidirect |
| 3. #22582908 | C2 | semidirect |
| 4. #22582898 | C2 | semidirect |
| 5. C2×Dic1124 | C2 | semidirect |
| 6. Q16×D281 | C2 | semidirect |
| 7. #22582885 | C2 | semidirect |
| 8. #135×C281 | C2 | semidirect |
| 59. C281 | #578 | semidirect |
| 65. #135 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582926 | 2 |
| #22582909 | 2 |
| #22582908 | 2 |
| #22582898 | 2 |
| C2×Dic1124 | 2 |
| Q16×D281 | 2 |
| #22582885 | 2 |
| #135×C281 | 2 |
| #578 | 281 |