Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
654 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22597249 | C2 | semidirect |
| 2. #22596983 | C2 | semidirect |
| 3. #22589892 | C2 | semidirect |
| 4. #22589646 | C2 | semidirect |
| 6. #22589042 | C2 | semidirect |
| 7. #22588842 | C2 | semidirect |
| 8. #22588703 | C2 | semidirect |
| 9. #22588627 | C2 | semidirect |
| 10. #22588490 | C2 | semidirect |
| 11. C71×#2103 | C2 | semidirect |
| 193. #2103 | D71 | semidirect |
| 202. C71 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597249 | 2 |
| #22596983 | 2 |
| #22589892 | 2 |
| #22589646 | 2 |
| #22589445 | 2 |
| #22589042 | 2 |
| #22588842 | 2 |
| #22588703 | 2 |
| #22588627 | 2 |
| #22588490 | 2 |
| C71×#2103 | 2 |
| #29386 | 71 |