Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1198 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 183 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. #22620018 | C2 | semidirect |
| 2. #22613214 | C2 | semidirect |
| 3. #22608968 | C2 | semidirect |
| 4. #22608866 | C2 | semidirect |
| 5. #22608439 | C2 | semidirect |
| 6. #22608275 | C2 | semidirect |
| 7. C73×#3497 | C2 | semidirect |
| 199. #3497 | D73 | semidirect |
| 206. C73 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620018 | 2 |
| #22613214 | 2 |
| #22608968 | 2 |
| #22608866 | 2 |
| #22608439 | 2 |
| #22608275 | 2 |
| C73×#3497 | 2 |
| #18186 | 73 |