Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
712 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16863686 | C2 | semidirect |
| 2. #22561010 | C2 | semidirect |
| 3. C2×D4⋊(C67⋊C8) | C2 | semidirect |
| 4. #22558092 | C2 | semidirect |
| 25. #14524043 | D4 | semidirect |
| 29. C4⋊(C67⋊C8) | D4 | semidirect |
| 164. C67 | #10235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863686 | 2 |
| #22561010 | 2 |
| C2×D4⋊(C67⋊C8) | 2 |
| #22558092 | 2 |
| C67×#2537 | 2 |
| #10235 | 67 |