Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17984863 | C2 | semidirect |
| 2. #22581504 | C2 | semidirect |
| 3. C4×#14555784 | C2 | semidirect |
| 4. #22581178 | C2 | semidirect |
| 5. #22581170 | C2 | semidirect |
| 6. #22581160 | C2 | semidirect |
| 7. #22581154 | C2 | semidirect |
| 8. #22581148 | C2 | semidirect |
| 9. C4⋊C8×D139 | C2 | semidirect |
| 10. #22580948 | C2 | semidirect |
| 11. #461×C139 | C2 | semidirect |
| 47. #14555784 | D4 | semidirect |
| 136. C4×C139 | #135 | semidirect |
| 150. C139 | #3035 | semidirect |
| 158. #461 | D139 | semidirect |
| 292. C4 | #17984863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984863 | 2 |
| #22581504 | 2 |
| C4×#14555784 | 2 |
| #22581178 | 2 |
| #22581170 | 2 |
| #22581160 | 2 |
| #22581154 | 2 |
| #22581148 | 2 |
| C4⋊C8×D139 | 2 |
| #22580948 | 2 |
| #461×C139 | 2 |
| #3035 | 139 |