Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22571152 | C2 | semidirect |
| 2. #22570008 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558707 | C2 | semidirect |
| 6. #22558599 | C2 | semidirect |
| 7. C67×#1303 | C2 | semidirect |
| 38. #14524043 | D4 | semidirect |
| 39. #14524043 | D4 | semidirect |
| 73. C4⋊C8×C67 | D4 | semidirect |
| 74. C4⋊C8×C67 | D4 | semidirect |
| 102. C2×D268 | SD16 | semidirect |
| 228. #1303 | D67 | semidirect |
| 229. C67 | #10246 | semidirect |
| 290. C4⋊C8 | D268 | semidirect |
| 291. C4⋊C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571152 | 2 |
| #22570008 | 2 |
| #22565151 | 2 |
| #22558878 | 2 |
| #22558707 | 2 |
| #22558599 | 2 |
| C67×#1303 | 2 |
| #10246 | 67 |