Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22601476 | C2 | semidirect |
| 2. #22597921 | C2 | semidirect |
| 3. #22590077 | C2 | semidirect |
| 4. #22586442 | C2 | semidirect |
| 5. C71×#2112 | C2 | semidirect |
| 26. C2×Dic284 | D4 | semidirect |
| 28. C2×D568 | D4 | semidirect |
| 39. #14556060 | D4 | semidirect |
| 52. C2×C16×C71 | D4 | semidirect |
| 146. #2112 | D71 | semidirect |
| 148. C71 | #13309 | semidirect |
| 191. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| #22597921 | 2 |
| #22590077 | 2 |
| #22586442 | 2 |
| C71×#2112 | 2 |
| #13309 | 71 |