Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
232 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 95 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. C16×Dic134 | C2 | semidirect |
| 3. #22558278 | C2 | semidirect |
| 4. #22558187 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 45. #11761616 | C16 | semidirect |
| 80. Dic134 | C2×C16 | semidirect |
| 88. C67⋊C8 | C2×C16 | semidirect |
| 113. C67 | SD16⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic134 | 2 |
| C8×#11761616 | 2 |
| #22558278 | 2 |
| #22558187 | 2 |
| D4⋊(C67⋊C16) | 2 |
| #22558128 | 2 |
| D4×C16×C67 | 2 |
| SD16⋊C16 | 67 |