Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
590 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22599470 | C2 | semidirect |
| 3. #22593509 | C2 | semidirect |
| 4. #22587026 | C2 | semidirect |
| 5. #22586834 | C2 | semidirect |
| 6. #22586730 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 220. #1303 | D71 | semidirect |
| 221. C71 | #10241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599470 | 2 |
| #22597806 | 2 |
| #22593509 | 2 |
| #22587026 | 2 |
| #22586834 | 2 |
| #22586730 | 2 |
| C71×#1303 | 2 |
| #10241 | 71 |