Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22598864 | C2 | semidirect |
| 4. #22586455 | C2 | semidirect |
| 5. C71×#1375 | C2 | semidirect |
| 20. C2×Dic284 | Q8 | semidirect |
| 22. C2×D568 | Q8 | semidirect |
| 123. #1375 | D71 | semidirect |
| 124. C71 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598864 | 2 |
| #22590077 | 2 |
| #22589233 | 2 |
| #22586455 | 2 |
| C71×#1375 | 2 |
| #13373 | 71 |