Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17984875 | C2 | semidirect |
| 3. C22×#14555774 | C2 | semidirect |
| 4. C2×#17984760 | C2 | semidirect |
| 5. C2×#17984758 | C2 | semidirect |
| 6. #22580919 | C2 | semidirect |
| 7. #341×C139 | C2 | semidirect |
| 127. C139 | #2019 | semidirect |
| 135. #341 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| C2×#17984870 | 2 |
| C22×#14555774 | 2 |
| C2×#17984760 | 2 |
| C2×#17984758 | 2 |
| #22580919 | 2 |
| #341×C139 | 2 |
| #2019 | 139 |