Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #22581361 | C2 | semidirect |
| 4. #22581360 | C2 | semidirect |
| 5. #22581354 | C2 | semidirect |
| 6. #22581350 | C2 | semidirect |
| 44. C2×C139⋊C8 | Q8 | semidirect |
| 65. M16×C139 | Q8 | semidirect |
| 112. C139 | #3163 | semidirect |
| 159. M16 | Dic278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581581 | 2 |
| #22581361 | 2 |
| #22581360 | 2 |
| #22581354 | 2 |
| #22581350 | 2 |
| #22580995 | 2 |
| #22580989 | 2 |
| C2×#17984773 | 2 |
| #22580911 | 2 |
| #428×C139 | 2 |
| #3163 | 139 |