Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16863687 | C2 | semidirect |
| 3. #22561010 | C2 | semidirect |
| 4. C2×#16863123 | C2 | semidirect |
| 5. C67×#1296 | C2 | semidirect |
| 27. #14524043 | D4 | semidirect |
| 48. C4⋊C8×C67 | D4 | semidirect |
| 163. #1296 | D67 | semidirect |
| 164. C67 | #10235 | semidirect |
| 203. C4⋊C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863687 | 2 |
| #22565125 | 2 |
| #22561010 | 2 |
| C2×#16863123 | 2 |
| C67×#1296 | 2 |
| #10235 | 67 |