Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1198 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22602111 | C2 | semidirect |
| 2. #22598431 | C2 | semidirect |
| 3. #22587376 | C2 | semidirect |
| 4. #22587274 | C2 | semidirect |
| 5. #22586847 | C2 | semidirect |
| 6. #22586684 | C2 | semidirect |
| 7. C71×#2398 | C2 | semidirect |
| 201. #2398 | D71 | semidirect |
| 206. C71 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602111 | 2 |
| #22598431 | 2 |
| #22587376 | 2 |
| #22587274 | 2 |
| #22586847 | 2 |
| #22586684 | 2 |
| C71×#2398 | 2 |
| #18186 | 71 |