Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22580860 | C2 | semidirect |
| 3. #22580844 | C2 | semidirect |
| 4. #22580842 | C2 | semidirect |
| 6. #22580827 | C2 | semidirect |
| 7. #22580824 | C2 | semidirect |
| 8. #22580817 | C2 | semidirect |
| 9. #391×C139 | C2 | semidirect |
| 12. #17984831 | C4 | semidirect |
| 48. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 49. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic139 | C2×C4 | semidirect |
| 54. C2×Q8×C139 | C2×C4 | semidirect |
| 123. C139 | #2379 | semidirect |
| 127. #391 | D139 | semidirect |
| 159. C2×Q8 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984831 | 2 |
| #22580860 | 2 |
| #22580844 | 2 |
| #22580842 | 2 |
| #22580831 | 2 |
| #22580827 | 2 |
| #22580824 | 2 |
| #22580817 | 2 |
| #391×C139 | 2 |
| #2379 | 139 |