Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581624 | C2 | semidirect |
| 3. #22581300 | C2 | semidirect |
| 4. #22581278 | C2 | semidirect |
| 5. #22581249 | C2 | semidirect |
| 6. #22581189 | C2 | semidirect |
| 7. #22581149 | C2 | semidirect |
| 8. #22581100 | C2 | semidirect |
| 9. C4×#14555774 | C2 | semidirect |
| 10. #22580950 | C2 | semidirect |
| 11. C8×D4×C139 | C2 | semidirect |
| 132. C139 | #3305 | semidirect |
| 143. C8×D4 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581624 | 2 |
| #22581300 | 2 |
| #22581278 | 2 |
| #22581249 | 2 |
| #22581189 | 2 |
| #22581149 | 2 |
| #22581100 | 2 |
| C4×#14555774 | 2 |
| #22580950 | 2 |
| C8×D4×C139 | 2 |
| #3305 | 139 |