Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22588143 | C2 | semidirect |
| 5. #22588142 | C2 | semidirect |
| 6. #22586469 | C2 | semidirect |
| 7. C71×#1395 | C2 | semidirect |
| 8. C2×#14556136 | C4 | semidirect |
| 15. #17986022 | C4 | semidirect |
| 18. #17985965 | C4 | semidirect |
| 21. C2×C8×Dic71 | C4 | semidirect |
| 22. #17985797 | C4 | semidirect |
| 23. #17985795 | C4 | semidirect |
| 212. #1395 | D71 | semidirect |
| 213. C71 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597048 | 2 |
| #22590023 | 2 |
| #22590003 | 2 |
| #22588143 | 2 |
| #22588142 | 2 |
| #22586469 | 2 |
| C71×#1395 | 2 |
| #12633 | 71 |