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. #22582927 | C2 | semidirect |
| 2. #22582926 | C2 | semidirect |
| 3. #22582912 | C2 | semidirect |
| 4. #22582911 | C2 | semidirect |
| 5. #22582908 | C2 | semidirect |
| 6. #22582900 | C2 | semidirect |
| 7. #22582899 | C2 | semidirect |
| 8. C2×#17985128 | C2 | semidirect |
| 9. Q16×D281 | C2 | semidirect |
| 10. #22582887 | C2 | semidirect |
| 11. #137×C281 | C2 | semidirect |
| 87. C281 | #578 | semidirect |
| 94. #137 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582927 | 2 |
| #22582926 | 2 |
| #22582912 | 2 |
| #22582911 | 2 |
| #22582908 | 2 |
| #22582900 | 2 |
| #22582899 | 2 |
| C2×#17985128 | 2 |
| Q16×D281 | 2 |
| #22582887 | 2 |
| #137×C281 | 2 |
| #578 | 281 |