Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22580927 | C2 | semidirect |
| 3. #22580747 | C2 | semidirect |
| 4. #22580745 | C2 | semidirect |
| 5. #410×C139 | C2 | semidirect |
| 6. C2×#14555785 | C4 | semidirect |
| 7. #17984840 | C4 | semidirect |
| 9. #17984831 | C4 | semidirect |
| 16. C2×C4×Dic139 | C4 | semidirect |
| 113. C139 | #2126 | semidirect |
| 117. #410 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581499 | 2 |
| #22580927 | 2 |
| #22580747 | 2 |
| #22580745 | 2 |
| #410×C139 | 2 |
| #2126 | 139 |