Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22601474 | C2 | semidirect |
| 2. #22598060 | C2 | semidirect |
| 3. C2×#17985808 | C2 | semidirect |
| 4. #22590068 | C2 | semidirect |
| 5. #22589968 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C71×#3060 | C2 | semidirect |
| 43. C2×Dic284 | D4 | semidirect |
| 45. C2×D568 | D4 | semidirect |
| 56. C2×C71⋊C16 | D4 | semidirect |
| 58. #14556064 | D4 | semidirect |
| 229. #3060 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22598060 | 2 |
| C2×#17985808 | 2 |
| #22590068 | 2 |
| #22589968 | 2 |
| #22586438 | 2 |
| C71×#3060 | 2 |
| #13318 | 71 |