Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#17984776 | C2 | semidirect |
| 2. C2×#17984774 | C2 | semidirect |
| 6. #22580819 | C2 | semidirect |
| 7. #336×C139 | C2 | semidirect |
| 99. C139 | #2092 | semidirect |
| 107. #336 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984776 | 2 |
| C2×#17984774 | 2 |
| C2×#17984764 | 2 |
| #22580855 | 2 |
| #22580819 | 2 |
| #336×C139 | 2 |
| #2092 | 139 |