Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
316 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17984776 | C2 | semidirect |
| 3. C2×#17984774 | C2 | semidirect |
| 5. #22580716 | C2 | semidirect |
| 6. #22580716 | C2 | semidirect |
| 23. C22⋊C8×C139 | C4 | semidirect |
| 120. C139 | #1854 | semidirect |
| 143. C22⋊C8 | Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984801 | 2 |
| C2×#17984776 | 2 |
| C2×#17984774 | 2 |
| #22580813 | 2 |
| #22580716 | 2 |
| C2×C22⋊C8×C139 | 2 |
| #1854 | 139 |