Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22573343 | C2 | semidirect |
| 2. #22569790 | C2 | semidirect |
| 3. #22561945 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22561820 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#3050 | C2 | semidirect |
| 38. C2×Dic268 | D4 | semidirect |
| 40. C2×D536 | D4 | semidirect |
| 56. C2×C67⋊C16 | D4 | semidirect |
| 58. #14523975 | D4 | semidirect |
| 67. C2×Q16×C67 | D4 | semidirect |
| 69. C2×D8×C67 | D4 | semidirect |
| 85. #106×C67 | D4 | semidirect |
| 235. #3050 | D67 | semidirect |
| 240. C67 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D67 | semidirect |
| 282. C2×D8 | C22⋊D67 | semidirect |
| 316. #106 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| #22569790 | 2 |
| #22561945 | 2 |
| #22561944 | 2 |
| #22561820 | 2 |
| #22558310 | 2 |
| C67×#3050 | 2 |
| #13309 | 67 |