Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22583608 | C2 | semidirect |
| 3. #22583605 | C2 | semidirect |
| 4. #22583605 | C2 | semidirect |
| 5. #22583603 | C2 | semidirect |
| 6. #22583603 | C2 | semidirect |
| 7. #22583601 | C2 | semidirect |
| 8. #22583600 | C2 | semidirect |
| 12. #22583589 | C2 | semidirect |
| 13. #22583588 | C2 | semidirect |
| 14. #22583586 | C2 | semidirect |
| 15. C22⋊Q8×C283 | C2 | semidirect |
| 97. C283 | #563 | semidirect |
| 113. 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 |
| #22583608 | 2 |
| #22583605 | 2 |
| #22583603 | 2 |
| #22583601 | 2 |
| #22583600 | 2 |
| #22583596 | 2 |
| #22583593 | 2 |
| #22583592 | 2 |
| #22583589 | 2 |
| #22583588 | 2 |
| #22583586 | 2 |
| C22⋊Q8×C283 | 2 |
| #563 | 283 |