Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 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. #22580853 | C2 | semidirect |
| 3. #22580843 | C2 | semidirect |
| 4. #22580838 | C2 | semidirect |
| 5. #22580831 | C2 | semidirect |
| 6. #22580829 | C2 | semidirect |
| 7. #22580824 | C2 | semidirect |
| 8. #22580816 | C2 | semidirect |
| 9. #380×C139 | C2 | semidirect |
| 13. #17984816 | C4 | semidirect |
| 37. C2×C22⋊D139 | C2×C4 | semidirect |
| 44. C4⋊Dic139 | C2×C4 | semidirect |
| 50. (C2×D139)⋊C4 | C2×C4 | semidirect |
| 54. C22×C4×C139 | C2×C4 | semidirect |
| 129. C139 | #2377 | semidirect |
| 139. #380 | D139 | semidirect |
| 176. C22×C4 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984816 | 2 |
| #22580853 | 2 |
| #22580843 | 2 |
| #22580838 | 2 |
| #22580831 | 2 |
| #22580829 | 2 |
| #22580824 | 2 |
| #22580816 | 2 |
| #380×C139 | 2 |
| #2377 | 139 |