Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22563117 | C2 | semidirect |
| 3. #22558704 | C2 | semidirect |
| 4. #22558601 | C2 | semidirect |
| 5. #22558111 | C2 | semidirect |
| 6. #22558067 | C2 | semidirect |
| 7. C67×#1517 | C2 | semidirect |
| 12. #16863598 | C4 | semidirect |
| 13. #16863588 | C4 | semidirect |
| 51. C4⋊(C67⋊C8) | C2×C4 | semidirect |
| 60. C4⋊Q8×C67 | C2×C4 | semidirect |
| 61. #127×C67 | C2×C4 | semidirect |
| 217. #1517 | D67 | semidirect |
| 222. C67 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D67 | semidirect |
| 254. #127 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569669 | 2 |
| #22563117 | 2 |
| #22558704 | 2 |
| #22558601 | 2 |
| #22558111 | 2 |
| #22558067 | 2 |
| C67×#1517 | 2 |
| #9179 | 67 |