Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22571127 | C2 | semidirect |
| 2. #22569673 | C2 | semidirect |
| 3. #22558877 | C2 | semidirect |
| 4. #22558703 | C2 | semidirect |
| 5. #22558600 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#2541 | C2 | semidirect |
| 38. #14524043 | D4 | semidirect |
| 39. #14524040 | D4 | semidirect |
| 47. C4⋊(C67⋊C8) | D4 | semidirect |
| 48. C4⋊(C67⋊C8) | D4 | semidirect |
| 124. C2×D4×C67 | D8 | semidirect |
| 243. #2541 | D67 | semidirect |
| 248. C67 | #10238 | semidirect |
| 352. C2×D4 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571127 | 2 |
| #22569673 | 2 |
| #22558877 | 2 |
| #22558703 | 2 |
| #22558600 | 2 |
| #22558112 | 2 |
| C67×#2541 | 2 |
| #10238 | 67 |