Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. #22581719 | C2 | semidirect |
| 3. #22580958 | C2 | semidirect |
| 4. #22580926 | C2 | semidirect |
| 5. #22580710 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 7. #418×C139 | C2 | semidirect |
| 13. #17984838 | C4 | semidirect |
| 14. #17984829 | C4 | semidirect |
| 37. C2×C139⋊C8 | D4 | semidirect |
| 56. C2×C8×C139 | D4 | semidirect |
| 115. C139 | #1910 | semidirect |
| 120. #418 | D139 | semidirect |
| 165. C2×C8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581719 | 2 |
| #22581520 | 2 |
| #22580958 | 2 |
| #22580926 | 2 |
| #22580710 | 2 |
| #22580709 | 2 |
| #418×C139 | 2 |
| #1910 | 139 |