Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 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. #22598060 | C2 | semidirect |
| 3. #22598002 | C2 | semidirect |
| 4. C2×#17985810 | C2 | semidirect |
| 5. #22590069 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C71×#2117 | C2 | semidirect |
| 49. C2×Dic284 | D4 | semidirect |
| 53. C2×D568 | D4 | semidirect |
| 66. #14556064 | D4 | semidirect |
| 87. C2×C16×C71 | D4 | semidirect |
| 232. #2117 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 306. 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 |
| #22598060 | 2 |
| #22598002 | 2 |
| C2×#17985810 | 2 |
| #22590069 | 2 |
| #22586439 | 2 |
| C71×#2117 | 2 |
| #13318 | 71 |