Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22590621 | C2 | semidirect |
| 3. #22586547 | C2 | semidirect |
| 4. #22586537 | C2 | semidirect |
| 7. C71×#1426 | C2 | semidirect |
| 22. Dic568 | Q8 | semidirect |
| 24. D1136 | Q8 | semidirect |
| 81. #1426 | D71 | semidirect |
| 85. C71 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590621 | 2 |
| #22590220 | 2 |
| #22586547 | 2 |
| #22586537 | 2 |
| #22586528 | 2 |
| #22586526 | 2 |
| C71×#1426 | 2 |
| #13710 | 71 |