Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 2. #22581357 | C2 | semidirect |
| 3. #22581331 | C2 | semidirect |
| 4. #22581302 | C2 | semidirect |
| 8. C4×Dic556 | C2 | semidirect |
| 9. C4×#14555775 | C2 | semidirect |
| 11. C4×Q16×C139 | C2 | semidirect |
| 83. C4×D139 | Q16 | semidirect |
| 114. C139 | #3170 | semidirect |
| 125. C4×Q16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581507 | 2 |
| #22581357 | 2 |
| #22581331 | 2 |
| #22581302 | 2 |
| #22581195 | 2 |
| #22581193 | 2 |
| #22581191 | 2 |
| C4×Dic556 | 2 |
| C4×#14555775 | 2 |
| C4×C8×D139 | 2 |
| C4×Q16×C139 | 2 |
| #3170 | 139 |