Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22581257 | C2 | semidirect |
| 3. #22581250 | C2 | semidirect |
| 4. #22581245 | C2 | semidirect |
| 5. #22581230 | C2 | semidirect |
| 6. #22580996 | C2 | semidirect |
| 7. C2×#17984775 | C2 | semidirect |
| 8. #22580980 | C2 | semidirect |
| 11. #544×C139 | C2 | semidirect |
| 42. #14555785 | Q8 | semidirect |
| 123. C139 | #3083 | semidirect |
| 125. #544 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581433 | 2 |
| #22581257 | 2 |
| #22581250 | 2 |
| #22581245 | 2 |
| #22581230 | 2 |
| #22580996 | 2 |
| C2×#17984775 | 2 |
| #22580980 | 2 |
| #22580952 | 2 |
| #22580947 | 2 |
| #544×C139 | 2 |
| #3083 | 139 |