Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
340 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22562458 | C2 | semidirect |
| 2. #22562432 | C2 | semidirect |
| 3. #22559801 | C2 | semidirect |
| 4. #22558127 | C2 | semidirect |
| 5. C67×#1712 | C2 | semidirect |
| 68. C8×C67 | D16 | semidirect |
| 89. #1712 | D67 | semidirect |
| 92. C67 | #12525 | semidirect |
| 155. C8 | #14523984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562458 | 2 |
| #22562432 | 2 |
| #22559801 | 2 |
| #22558127 | 2 |
| C67×#1712 | 2 |
| #12525 | 67 |