Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. C2×#16863218 | C2 | semidirect |
| 5. #22561000 | C2 | semidirect |
| 6. #22558296 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 21. #16863202 | C4 | semidirect |
| 44. C2×C67⋊C16 | C2×C4 | semidirect |
| 59. #108×C67 | C2×C4 | semidirect |
| 157. #1383 | D67 | semidirect |
| 159. C67 | #12949 | semidirect |
| 207. #108 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569092 | 2 |
| C2×#16863218 | 2 |
| #22561959 | 2 |
| #22561936 | 2 |
| #22561000 | 2 |
| #22558296 | 2 |
| C67×#1383 | 2 |
| #12949 | 67 |