Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22580957 | C2 | semidirect |
| 3. C2×#17984759 | C2 | semidirect |
| 4. #22580712 | C2 | semidirect |
| 5. #518×C139 | C2 | semidirect |
| 10. #17984838 | C4 | semidirect |
| 22. C2×D556 | C2×C4 | semidirect |
| 30. C4×Dic139 | C2×C4 | semidirect |
| 38. C4⋊C4×C139 | D4 | semidirect |
| 87. C139 | #1887 | semidirect |
| 90. #518 | D139 | semidirect |
| 124. C4⋊C4 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984838 | 2 |
| #22580957 | 2 |
| C2×#17984759 | 2 |
| #22580712 | 2 |
| #518×C139 | 2 |
| #1887 | 139 |