Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22581329 | C2 | semidirect |
| 2. #22581148 | C2 | semidirect |
| 3. D4×C139⋊C8 | C2 | semidirect |
| 4. #22580705 | C2 | semidirect |
| 5. #22580697 | C2 | semidirect |
| 6. #22580696 | C2 | semidirect |
| 7. #459×C139 | C2 | semidirect |
| 53. C139⋊C8 | D8 | semidirect |
| 62. D4×C139 | D8 | semidirect |
| 92. C139 | #1667 | semidirect |
| 96. #459 | D139 | semidirect |
| 151. D4 | #14555770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581329 | 2 |
| #22581148 | 2 |
| D4×C139⋊C8 | 2 |
| #22580705 | 2 |
| #22580697 | 2 |
| #22580696 | 2 |
| #459×C139 | 2 |
| #1667 | 139 |