Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581660 | C2 | semidirect |
| 2. #22581624 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581300 | C2 | semidirect |
| 5. #22581256 | C2 | semidirect |
| 6. #22581243 | C2 | semidirect |
| 7. #22581148 | C2 | semidirect |
| 8. #22581146 | C2 | semidirect |
| 9. #22581083 | C2 | semidirect |
| 10. #22581062 | C2 | semidirect |
| 11. C4×D8×C139 | C2 | semidirect |
| 94. D4×C139 | #41 | semidirect |
| 129. C139 | #3366 | semidirect |
| 141. C4×D8 | D139 | semidirect |
| 218. D4 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581660 | 2 |
| #22581624 | 2 |
| #22581316 | 2 |
| #22581300 | 2 |
| #22581256 | 2 |
| #22581243 | 2 |
| #22581148 | 2 |
| #22581146 | 2 |
| #22581083 | 2 |
| #22581062 | 2 |
| C4×D8×C139 | 2 |
| #3366 | 139 |