Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#17985380 | C2 | semidirect |
| 2. C2×#17985375 | C2 | semidirect |
| 3. #22583590 | C2 | semidirect |
| 5. #22583543 | C2 | semidirect |
| 6. #22583535 | C2 | semidirect |
| 7. #102×C283 | C2 | semidirect |
| 30. C283⋊C8 | D4 | semidirect |
| 55. C283 | #468 | semidirect |
| 63. #102 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985380 | 2 |
| C2×#17985375 | 2 |
| #22583590 | 2 |
| #22583581 | 2 |
| #22583543 | 2 |
| #22583535 | 2 |
| #102×C283 | 2 |
| #468 | 283 |