Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569925 | C2 | semidirect |
| 2. #22569867 | C2 | semidirect |
| 3. C2×#16863206 | C2 | semidirect |
| 4. #22561937 | C2 | semidirect |
| 5. #22561836 | C2 | semidirect |
| 6. #22558308 | C2 | semidirect |
| 7. C67×#3414 | C2 | semidirect |
| 57. #14523979 | D4 | semidirect |
| 75. C2×Q16×C67 | D4 | semidirect |
| 79. C2×D8×C67 | D4 | semidirect |
| 87. C2×C16×C67 | D4 | semidirect |
| 227. #3414 | D67 | semidirect |
| 234. C67 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D67 | semidirect |
| 281. C2×D8 | C22⋊D67 | semidirect |
| 306. C2×C16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569925 | 2 |
| #22569867 | 2 |
| C2×#16863206 | 2 |
| #22561937 | 2 |
| #22561836 | 2 |
| #22558308 | 2 |
| C67×#3414 | 2 |
| #13318 | 67 |