Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22581431 | C2 | semidirect |
| 5. #22580725 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 7. #419×C139 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 12. C2×#14555772 | C4 | semidirect |
| 109. C139 | #1905 | semidirect |
| 114. #419 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984873 | 2 |
| #22581431 | 2 |
| #22580969 | 2 |
| #22580926 | 2 |
| #22580725 | 2 |
| #22580709 | 2 |
| #419×C139 | 2 |
| #1905 | 139 |