Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581676 | C2 | semidirect |
| 2. #22581663 | C2 | semidirect |
| 3. #22581308 | C2 | semidirect |
| 4. #22581304 | C2 | semidirect |
| 5. #22581261 | C2 | semidirect |
| 6. #22581244 | C2 | semidirect |
| 8. #22581159 | C2 | semidirect |
| 9. C4×#14555774 | C2 | semidirect |
| 11. C8×Q8×C139 | C2 | semidirect |
| 120. C139 | #3360 | semidirect |
| 130. C8×Q8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581663 | 2 |
| #22581308 | 2 |
| #22581304 | 2 |
| #22581261 | 2 |
| #22581244 | 2 |
| #22581169 | 2 |
| #22581159 | 2 |
| C4×#14555774 | 2 |
| C4×D1112 | 2 |
| C8×Q8×C139 | 2 |
| #3360 | 139 |