Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22563319 | C2 | semidirect |
| 3. #22558832 | C2 | semidirect |
| 4. #22558717 | C2 | semidirect |
| 5. #22558102 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#1505 | C2 | semidirect |
| 11. #16863788 | C4 | semidirect |
| 12. #16863783 | C4 | semidirect |
| 58. #14523954 | C2×C4 | semidirect |
| 66. C4⋊Q8×C67 | C2×C4 | semidirect |
| 67. #127×C67 | C2×C4 | semidirect |
| 231. #1505 | D67 | semidirect |
| 234. C67 | #9441 | semidirect |
| 271. C4⋊Q8 | C4×D67 | semidirect |
| 272. #127 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570677 | 2 |
| #22563319 | 2 |
| #22558832 | 2 |
| #22558717 | 2 |
| #22558102 | 2 |
| #22558101 | 2 |
| C67×#1505 | 2 |
| #9441 | 67 |