Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22581753 | C2 | semidirect |
| 2. C2×#17984864 | C2 | semidirect |
| 3. C2×#17984848 | C2 | semidirect |
| 4. #22581229 | C2 | semidirect |
| 5. #22581224 | C2 | semidirect |
| 6. #22581217 | C2 | semidirect |
| 7. #22580935 | C2 | semidirect |
| 8. C2×#108×C139 | C2 | semidirect |
| 20. C2×Dic556 | C22 | semidirect |
| 21. C2×#14555774 | C22 | semidirect |
| 22. C2×D1112 | C22 | semidirect |
| 30. #17984760 | C22 | semidirect |
| 31. #17984758 | C22 | semidirect |
| 34. #108×C139 | C22 | semidirect |
| 35. #108×C139 | C22 | semidirect |
| 132. C139 | #3067 | semidirect |
| 140. C2×#108 | D139 | semidirect |
| 165. #108 | C2×D139 | semidirect |
| 166. #108 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| C2×#17984864 | 2 |
| C2×#17984848 | 2 |
| #22581229 | 2 |
| #22581224 | 2 |
| #22581217 | 2 |
| #22580935 | 2 |
| C2×#108×C139 | 2 |
| #3067 | 139 |