Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #22571124 | C2 | semidirect |
| 2. #22569669 | C2 | semidirect |
| 3. #22565151 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558601 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#1502 | C2 | semidirect |
| 58. C4⋊(C67⋊C8) | D4 | semidirect |
| 59. C4⋊(C67⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C67 | D4 | semidirect |
| 67. #127×C67 | D4 | semidirect |
| 102. C2×D268 | D8 | semidirect |
| 245. #1502 | D67 | semidirect |
| 248. C67 | #10238 | semidirect |
| 285. C4⋊Q8 | D268 | semidirect |
| 292. #127 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22569669 | 2 |
| #22565151 | 2 |
| #22558876 | 2 |
| #22558601 | 2 |
| #22558112 | 2 |
| C67×#1502 | 2 |
| #10238 | 67 |