Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22573346 | C2 | semidirect |
| 2. #22562524 | C2 | semidirect |
| 3. C2×#16863231 | C2 | semidirect |
| 4. #22562330 | C2 | semidirect |
| 5. #22558392 | C2 | semidirect |
| 6. #22558352 | C2 | semidirect |
| 7. C67×#1419 | C2 | semidirect |
| 13. C2×D1072 | C22 | semidirect |
| 20. C2×C67⋊C32 | C22 | semidirect |
| 23. M64×C67 | C22 | semidirect |
| 24. #368×C67 | C22 | semidirect |
| 126. #1419 | D67 | semidirect |
| 129. C67 | #13669 | semidirect |
| 143. M64 | C2×D67 | semidirect |
| 145. #368 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573346 | 2 |
| #22562524 | 2 |
| C2×#16863231 | 2 |
| #22562330 | 2 |
| #22558392 | 2 |
| #22558352 | 2 |
| C67×#1419 | 2 |
| #13669 | 67 |