Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16863791 | C2 | semidirect |
| 2. C2×#16863755 | C2 | semidirect |
| 3. #22561181 | C2 | semidirect |
| 4. C2×#16863136 | C2 | semidirect |
| 5. C2×#16863136 | C2 | semidirect |
| 6. #22558090 | C2 | semidirect |
| 42. #14524043 | D4 | semidirect |
| 51. #14523954 | D4 | semidirect |
| 52. #14523954 | D4 | semidirect |
| 218. C67 | #10081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863791 | 2 |
| C2×#16863755 | 2 |
| #22561181 | 2 |
| C2×#16863136 | 2 |
| #22558090 | 2 |
| C67×#2819 | 2 |
| #10081 | 67 |