Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×D536 | C2 | semidirect |
| 2. #22562458 | C2 | semidirect |
| 3. #22562241 | C2 | semidirect |
| 4. #22558254 | C2 | semidirect |
| 5. #22558169 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 7. C67×#1667 | C2 | semidirect |
| 17. C4⋊(C67⋊C16) | C22 | semidirect |
| 19. C4×C67⋊C16 | C22 | semidirect |
| 20. #493×C67 | C22 | semidirect |
| 23. #335×C67 | C22 | semidirect |
| 73. D536 | D8 | semidirect |
| 110. D4×C67 | D16 | semidirect |
| 166. #1667 | D67 | semidirect |
| 170. C67 | #12316 | semidirect |
| 176. #493 | C2×D67 | semidirect |
| 186. #335 | C2×D67 | semidirect |
| 282. D4 | #14523984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D536 | 2 |
| #22562458 | 2 |
| #22562241 | 2 |
| #22558254 | 2 |
| #22558169 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#1667 | 2 |
| #12316 | 67 |