Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C22×#14555775 | C2 | semidirect |
| 3. C2×#17984767 | C2 | semidirect |
| 5. #22580860 | C2 | semidirect |
| 6. #22580707 | C2 | semidirect |
| 125. C139 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555775 | 2 |
| C2×#17984829 | 2 |
| C2×#17984767 | 2 |
| C2×#17984763 | 2 |
| #22580860 | 2 |
| #22580707 | 2 |
| C22×SD16×C139 | 2 |
| #2015 | 139 |