Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22562484 | C2 | semidirect |
| 3. #22562433 | C2 | semidirect |
| 4. #22559801 | C2 | semidirect |
| 5. C8×C16×C67 | C2 | semidirect |
| 45. C16×C67 | SD16 | semidirect |
| 57. C8×C67 | D16 | semidirect |
| 78. C8×C16 | D67 | semidirect |
| 79. C67 | #12503 | semidirect |
| 119. C16 | #11761617 | semidirect |
| 131. C8 | D1072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562484 | 2 |
| #22562459 | 2 |
| #22562433 | 2 |
| #22559801 | 2 |
| C8×C16×C67 | 2 |
| #12503 | 67 |