Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #22581427 | C2 | semidirect |
| 3. #22580971 | C2 | semidirect |
| 4. #22580969 | C2 | semidirect |
| 5. C2×#17984758 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 7. H(3,ℤ/4)×C139 | C2 | semidirect |
| 11. #17984839 | C4 | semidirect |
| 12. #17984830 | C4 | semidirect |
| 30. C2×Dic278 | C2×C4 | semidirect |
| 37. C2×D556 | C2×C4 | semidirect |
| 49. C4×Dic139 | D4 | semidirect |
| 58. C42×C139 | C2×C4 | semidirect |
| 59. C42×C139 | D4 | semidirect |
| 116. C139 | #1911 | semidirect |
| 124. H(3,ℤ/4) | D139 | semidirect |
| 175. C42 | C4×D139 | semidirect |
| 176. C42 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581522 | 2 |
| #22581427 | 2 |
| #22580971 | 2 |
| #22580969 | 2 |
| C2×#17984758 | 2 |
| #22580709 | 2 |
| H(3,ℤ/4)×C139 | 2 |
| #1911 | 139 |