Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22599550 | C2 | semidirect |
| 4. #22586812 | C2 | semidirect |
| 6. #22586201 | C2 | semidirect |
| 7. C71×#1537 | C2 | semidirect |
| 191. #1537 | D71 | semidirect |
| 195. C71 | #10043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599550 | 2 |
| #22598440 | 2 |
| #22598344 | 2 |
| #22586812 | 2 |
| #22586680 | 2 |
| #22586201 | 2 |
| C71×#1537 | 2 |
| #10043 | 71 |