Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 2. C8×Dic268 | C2 | semidirect |
| 4. #22558281 | C2 | semidirect |
| 5. #22558174 | C2 | semidirect |
| 7. C67×#1311 | C2 | semidirect |
| 28. #14523988 | C8 | semidirect |
| 48. Dic268 | C2×C8 | semidirect |
| 67. C16×C67 | C2×C8 | semidirect |
| 112. #1311 | D67 | semidirect |
| 113. C67 | #12043 | semidirect |
| 173. C16 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523988 | 2 |
| C8×Dic268 | 2 |
| C8×D536 | 2 |
| #22558281 | 2 |
| #22558174 | 2 |
| #22558171 | 2 |
| C67×#1311 | 2 |
| #12043 | 67 |