Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 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. #22601474 | C2 | semidirect |
| 2. #22598061 | C2 | semidirect |
| 3. #22597998 | C2 | semidirect |
| 4. C2×#17985810 | C2 | semidirect |
| 5. #22589969 | C2 | semidirect |
| 6. #22586440 | C2 | semidirect |
| 7. C71×#2143 | C2 | semidirect |
| 44. C2×Dic284 | D4 | semidirect |
| 46. C2×D568 | D4 | semidirect |
| 66. C2×C71⋊C16 | D4 | semidirect |
| 87. #108×C71 | D4 | semidirect |
| 231. #2143 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 308. #108 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22598061 | 2 |
| #22597998 | 2 |
| C2×#17985810 | 2 |
| #22589969 | 2 |
| #22586440 | 2 |
| C71×#2143 | 2 |
| #13318 | 71 |