Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22583609 | C2 | semidirect |
| 2. #22583605 | C2 | semidirect |
| 3. #22583599 | C2 | semidirect |
| 4. #22583596 | C2 | semidirect |
| 5. #22583592 | C2 | semidirect |
| 6. #22583590 | C2 | semidirect |
| 8. Q8×Dic283 | C2 | semidirect |
| 9. #22583572 | C2 | semidirect |
| 10. #22583569 | C2 | semidirect |
| 11. C22⋊Q8×C283 | C2 | semidirect |
| 73. C283 | #542 | semidirect |
| 81. C22⋊Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583609 | 2 |
| #22583605 | 2 |
| #22583599 | 2 |
| #22583596 | 2 |
| #22583592 | 2 |
| #22583590 | 2 |
| #22583584 | 2 |
| Q8×Dic283 | 2 |
| #22583572 | 2 |
| #22583569 | 2 |
| C22⋊Q8×C283 | 2 |
| #542 | 283 |