Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22570786 | C2 | semidirect |
| 2. #22562484 | C2 | semidirect |
| 3. #22562432 | C2 | semidirect |
| 4. #22562292 | C2 | semidirect |
| 5. D16×Dic67 | C2 | semidirect |
| 6. C4×C16×D67 | C2 | semidirect |
| 7. C67×#2246 | C2 | semidirect |
| 76. C16×C67 | #41 | semidirect |
| 95. C4×D67 | D16 | semidirect |
| 124. #2246 | D67 | semidirect |
| 129. C67 | #33733 | semidirect |
| 198. C16 | #11761627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570786 | 2 |
| #22562484 | 2 |
| #22562432 | 2 |
| #22562292 | 2 |
| D16×Dic67 | 2 |
| C4×C16×D67 | 2 |
| C67×#2246 | 2 |
| #33733 | 67 |