Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
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. #22583658 | C2 | semidirect |
| 2. #22583657 | C2 | semidirect |
| 3. #22583643 | C2 | semidirect |
| 4. #22583642 | C2 | semidirect |
| 5. #22583639 | C2 | semidirect |
| 6. #22583631 | C2 | semidirect |
| 7. #22583630 | C2 | semidirect |
| 8. C2×#17985382 | C2 | semidirect |
| 9. Q16×D283 | C2 | semidirect |
| 10. #22583618 | C2 | semidirect |
| 11. #137×C283 | C2 | semidirect |
| 87. C283 | #578 | semidirect |
| 94. #137 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583658 | 2 |
| #22583657 | 2 |
| #22583643 | 2 |
| #22583642 | 2 |
| #22583639 | 2 |
| #22583631 | 2 |
| #22583630 | 2 |
| C2×#17985382 | 2 |
| Q16×D283 | 2 |
| #22583618 | 2 |
| #137×C283 | 2 |
| #578 | 283 |