Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22610719 | C2 | semidirect |
| 5. #22608047 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 7. C73×#2155 | C2 | semidirect |
| 17. #17988401 | C4 | semidirect |
| 41. #14556527 | C2×C4 | semidirect |
| 50. M32×C73 | C2×C4 | semidirect |
| 139. #2155 | D73 | semidirect |
| 145. C73 | #12953 | semidirect |
| 181. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618782 | 2 |
| C2×#17988401 | 2 |
| C2×#17988399 | 2 |
| #22610719 | 2 |
| #22608047 | 2 |
| #22608018 | 2 |
| C73×#2155 | 2 |
| #12953 | 73 |