Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 3. #22581259 | C2 | semidirect |
| 4. #22581258 | C2 | semidirect |
| 5. #22581245 | C2 | semidirect |
| 6. #22581239 | C2 | semidirect |
| 7. #22581238 | C2 | semidirect |
| 11. #477×C139 | C2 | semidirect |
| 47. Q8×D139 | Q8 | semidirect |
| 130. C139 | #3078 | semidirect |
| 137. #477 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4×Q8×D139 | 2 |
| #22581259 | 2 |
| #22581258 | 2 |
| #22581245 | 2 |
| #22581239 | 2 |
| #22581238 | 2 |
| #22580994 | 2 |
| #22580975 | 2 |
| #22580960 | 2 |
| #477×C139 | 2 |
| #3078 | 139 |