Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22565155 | C2 | semidirect |
| 3. #22558878 | C2 | semidirect |
| 4. #22558704 | C2 | semidirect |
| 5. #22558600 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 7. C67×#3036 | C2 | semidirect |
| 47. C4⋊(C67⋊C8) | D4 | semidirect |
| 62. C4⋊Q8×C67 | D4 | semidirect |
| 63. #127×C67 | D4 | semidirect |
| 77. C4⋊C8×C67 | D4 | semidirect |
| 119. C2×D4×C67 | D8 | semidirect |
| 242. #3036 | D67 | semidirect |
| 248. C67 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D67 | semidirect |
| 292. #127 | C22⋊D67 | semidirect |
| 312. C4⋊C8 | C22⋊D67 | semidirect |
| 352. C2×D4 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22565155 | 2 |
| #22558878 | 2 |
| #22558704 | 2 |
| #22558600 | 2 |
| #22558110 | 2 |
| C67×#3036 | 2 |
| #10238 | 67 |