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 |
|---|---|---|
| 2. #22562572 | C2 | semidirect |
| 3. C4×#14523974 | C2 | semidirect |
| 4. #22560042 | C2 | semidirect |
| 6. #22559896 | C2 | semidirect |
| 10. C4×#11761616 | C4 | semidirect |
| 30. C4×Dic134 | C2×C4 | semidirect |
| 35. #14523974 | C2×C4 | semidirect |
| 36. #14523966 | C2×C4 | semidirect |
| 39. C4×C67⋊C8 | C2×C4 | semidirect |
| 56. #11761616 | C42 | semidirect |
| 129. C67 | #20506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11761616 | 2 |
| #22562572 | 2 |
| C4×#14523974 | 2 |
| #22560042 | 2 |
| #22560034 | 2 |
| #22559896 | 2 |
| C67×#2275 | 2 |
| #20506 | 67 |