Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
646 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22597250 | C2 | semidirect |
| 2. #22596987 | C2 | semidirect |
| 3. #22589921 | C2 | semidirect |
| 4. #22589893 | C2 | semidirect |
| 5. #22589643 | C2 | semidirect |
| 6. #22589054 | C2 | semidirect |
| 7. #22588843 | C2 | semidirect |
| 8. #22588704 | C2 | semidirect |
| 9. #22588625 | C2 | semidirect |
| 10. #22588490 | C2 | semidirect |
| 202. C71 | #29387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597250 | 2 |
| #22596987 | 2 |
| #22589921 | 2 |
| #22589893 | 2 |
| #22589643 | 2 |
| #22589054 | 2 |
| #22588843 | 2 |
| #22588704 | 2 |
| #22588625 | 2 |
| #22588490 | 2 |
| C71×#2017 | 2 |
| #29387 | 71 |