Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22583605 | C2 | semidirect |
| 2. #22583601 | C2 | semidirect |
| 3. #22583599 | C2 | semidirect |
| 4. #22583595 | C2 | semidirect |
| 5. #22583586 | C2 | semidirect |
| 7. C4×D1132 | C2 | semidirect |
| 8. C4×D1132 | C2 | semidirect |
| 9. #22583567 | C2 | semidirect |
| 10. C42×D283 | C2 | semidirect |
| 11. C4×Q8×C283 | C2 | semidirect |
| 74. C283 | #529 | semidirect |
| 82. C4×Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583605 | 2 |
| #22583601 | 2 |
| #22583599 | 2 |
| #22583595 | 2 |
| #22583586 | 2 |
| #22583585 | 2 |
| C4×D1132 | 2 |
| #22583567 | 2 |
| C42×D283 | 2 |
| C4×Q8×C283 | 2 |
| #529 | 283 |