Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581668 | C2 | semidirect |
| 2. #22581607 | C2 | semidirect |
| 3. #22581351 | C2 | semidirect |
| 4. #22581278 | C2 | semidirect |
| 5. #22581272 | C2 | semidirect |
| 6. #22581244 | C2 | semidirect |
| 7. #22581234 | C2 | semidirect |
| 8. #22581206 | C2 | semidirect |
| 9. C4×D1112 | C2 | semidirect |
| 10. #22580995 | C2 | semidirect |
| 11. #436×C139 | C2 | semidirect |
| 101. C8×C139 | #41 | semidirect |
| 127. C139 | #3354 | semidirect |
| 138. #436 | D139 | semidirect |
| 229. C8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581607 | 2 |
| #22581351 | 2 |
| #22581278 | 2 |
| #22581272 | 2 |
| #22581244 | 2 |
| #22581234 | 2 |
| #22581206 | 2 |
| C4×D1112 | 2 |
| #22580995 | 2 |
| #436×C139 | 2 |
| #3354 | 139 |