Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #22581676 | C2 | semidirect |
| 2. #22581315 | C2 | semidirect |
| 3. #22581305 | C2 | semidirect |
| 4. #22581245 | C2 | semidirect |
| 5. #22581230 | C2 | semidirect |
| 7. #22581158 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 9. #22581053 | C2 | semidirect |
| 11. D4×Q8×C139 | C2 | semidirect |
| 122. C139 | #3367 | semidirect |
| 125. D4×Q8 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581315 | 2 |
| #22581305 | 2 |
| #22581245 | 2 |
| #22581230 | 2 |
| #22581168 | 2 |
| #22581158 | 2 |
| #22581084 | 2 |
| #22581053 | 2 |
| C4×#14555770 | 2 |
| D4×Q8×C139 | 2 |
| #3367 | 139 |