Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984842 | C2 | semidirect |
| 3. #22581249 | C2 | semidirect |
| 4. #22581244 | C2 | semidirect |
| 5. #22581239 | C2 | semidirect |
| 6. #22581234 | C2 | semidirect |
| 7. #22580995 | C2 | semidirect |
| 9. #423×C139 | C2 | semidirect |
| 36. #14555785 | Q8 | semidirect |
| 74. Dic278 | C2×Q8 | semidirect |
| 76. D556 | C2×Q8 | semidirect |
| 121. C139 | #3079 | semidirect |
| 130. #423 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984842 | 2 |
| C4×#14555785 | 2 |
| #22581249 | 2 |
| #22581244 | 2 |
| #22581239 | 2 |
| #22581234 | 2 |
| #22580995 | 2 |
| #22580955 | 2 |
| #423×C139 | 2 |
| #3079 | 139 |