Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #22581678 | C2 | semidirect |
| 3. #22581303 | C2 | semidirect |
| 4. #22581302 | C2 | semidirect |
| 5. #22581239 | C2 | semidirect |
| 6. #22581236 | C2 | semidirect |
| 8. #22581077 | C2 | semidirect |
| 78. Dic278 | SD16 | semidirect |
| 118. C139 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581678 | 2 |
| D4×Dic278 | 2 |
| #22581303 | 2 |
| #22581302 | 2 |
| #22581239 | 2 |
| #22581236 | 2 |
| #22581156 | 2 |
| #22581077 | 2 |
| SD16×Dic139 | 2 |
| C4×#14555773 | 2 |
| #461×C139 | 2 |
| #3359 | 139 |