Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×#17984807 | C2 | semidirect |
| 3. #22580858 | C2 | semidirect |
| 4. #22580857 | C2 | semidirect |
| 10. C22×Dic278 | C4 | semidirect |
| 43. C22⋊Dic139 | Q8 | semidirect |
| 56. Dic278 | C22⋊C4 | semidirect |
| 67. C2×Dic139 | C2×Q8 | semidirect |
| 86. C22×C139 | C4×Q8 | semidirect |
| 105. C139 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #17984807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic278 | 2 |
| C2×#17984807 | 2 |
| #22580858 | 2 |
| #22580857 | 2 |
| #22580811 | 2 |
| C22⋊C4×Dic139 | 2 |
| C4×C22⋊Dic139 | 2 |
| #380×C139 | 2 |
| Q8×C22⋊C4 | 139 |