Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#17984768 | C2 | semidirect |
| 3. #22580955 | C2 | semidirect |
| 4. #22580818 | C2 | semidirect |
| 5. #343×C139 | C2 | semidirect |
| 33. C4×Dic139 | D4 | semidirect |
| 84. C139 | #2040 | semidirect |
| 90. #343 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581534 | 2 |
| C2×#17984768 | 2 |
| #22580955 | 2 |
| #22580818 | 2 |
| #343×C139 | 2 |
| #2040 | 139 |