Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22581154 | C2 | semidirect |
| 3. #22581150 | C2 | semidirect |
| 4. #22581080 | C2 | semidirect |
| 5. #22580703 | C2 | semidirect |
| 6. #22580696 | C2 | semidirect |
| 7. #331×C139 | C2 | semidirect |
| 55. C139⋊C8 | SD16 | semidirect |
| 86. C139 | #1688 | semidirect |
| 94. #331 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581329 | 2 |
| #22581154 | 2 |
| #22581150 | 2 |
| #22581080 | 2 |
| #22580703 | 2 |
| #22580696 | 2 |
| #331×C139 | 2 |
| #1688 | 139 |