Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
706 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22558038 | C2 | semidirect |
| 4. #22558037 | C2 | semidirect |
| 5. C67×#1274 | C2 | semidirect |
| 11. #16863447 | C4 | semidirect |
| 14. C4×#11761611 | C4 | semidirect |
| 40. C4×C67⋊C8 | C2×C4 | semidirect |
| 47. C4×C8×C67 | C2×C4 | semidirect |
| 75. C4×Dic67 | M16 | semidirect |
| 81. C42×C67 | M16 | semidirect |
| 141. #1274 | D67 | semidirect |
| 142. C67 | #7855 | semidirect |
| 182. C4×C8 | C4×D67 | semidirect |
| 218. C42 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568837 | 2 |
| #376×D67 | 2 |
| #22558038 | 2 |
| #22558037 | 2 |
| C67×#1274 | 2 |
| #7855 | 67 |