Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22562111 | C2 | semidirect |
| 4. #22558187 | C2 | semidirect |
| 6. #22558127 | C2 | semidirect |
| 7. C67×#1370 | C2 | semidirect |
| 47. #11761617 | C16 | semidirect |
| 80. Dic134 | C2×C16 | semidirect |
| 84. C8×C67 | C2×C16 | semidirect |
| 109. #1370 | D67 | semidirect |
| 113. C67 | SD16⋊C16 | semidirect |
| 192. C8 | C16×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562111 | 2 |
| #22562028 | 2 |
| C8×#11761617 | 2 |
| #22558187 | 2 |
| #22558163 | 2 |
| #22558127 | 2 |
| C67×#1370 | 2 |
| SD16⋊C16 | 67 |