Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#16863825 | C2 | semidirect |
| 2. #22570636 | C2 | semidirect |
| 3. #22562467 | C2 | semidirect |
| 4. #22562464 | C2 | semidirect |
| 5. #22562462 | C2 | semidirect |
| 6. C4×C16×D67 | C2 | semidirect |
| 7. C67×#2246 | C2 | semidirect |
| 42. C16×D67 | D4 | semidirect |
| 106. C4×C67 | #508 | semidirect |
| 122. #2246 | D67 | semidirect |
| 124. C67 | #33713 | semidirect |
| 226. C4 | #16863825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863825 | 2 |
| #22570636 | 2 |
| #22562467 | 2 |
| #22562464 | 2 |
| #22562462 | 2 |
| C4×C16×D67 | 2 |
| C67×#2246 | 2 |
| #33713 | 67 |