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. #22580857 | C2 | semidirect |
| 3. #22580845 | C2 | semidirect |
| 4. #22580843 | C2 | semidirect |
| 6. #22580827 | C2 | semidirect |
| 7. #22580824 | C2 | semidirect |
| 8. #22580819 | C2 | semidirect |
| 9. #382×C139 | C2 | semidirect |
| 13. #17984830 | C4 | semidirect |
| 35. C2×Dic278 | C2×C4 | semidirect |
| 51. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 52. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 61. C42×C139 | C2×C4 | semidirect |
| 127. C139 | #2379 | semidirect |
| 137. #382 | D139 | semidirect |
| 189. C42 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984830 | 2 |
| #22580857 | 2 |
| #22580845 | 2 |
| #22580843 | 2 |
| #22580831 | 2 |
| #22580827 | 2 |
| #22580824 | 2 |
| #22580819 | 2 |
| #382×C139 | 2 |
| #2379 | 139 |