Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
156 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22581245 | C2 | semidirect |
| 4. #22581080 | C2 | semidirect |
| 5. #22580705 | C2 | semidirect |
| 7. #333×C139 | C2 | semidirect |
| 76. C139 | #1698 | semidirect |
| 83. #333 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581301 | 2 |
| #22581245 | 2 |
| #22581154 | 2 |
| #22581080 | 2 |
| #22580705 | 2 |
| #22580696 | 2 |
| #333×C139 | 2 |
| #1698 | 139 |