Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 3. C4×#14523974 | C2 | semidirect |
| 4. #22560039 | C2 | semidirect |
| 6. #22559896 | C2 | semidirect |
| 7. C67×#2276 | C2 | semidirect |
| 10. C4×#11761615 | C4 | semidirect |
| 35. #14523974 | C2×C4 | semidirect |
| 36. #14523967 | C2×C4 | semidirect |
| 39. C4×C67⋊C8 | C2×C4 | semidirect |
| 43. C4×Q8×C67 | C2×C4 | semidirect |
| 58. #11761615 | C42 | semidirect |
| 123. #2276 | D67 | semidirect |
| 129. C67 | #20506 | semidirect |
| 154. C4×Q8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11761615 | 2 |
| #22562571 | 2 |
| C4×#14523974 | 2 |
| #22560039 | 2 |
| #22560037 | 2 |
| #22559896 | 2 |
| C67×#2276 | 2 |
| #20506 | 67 |