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. #22570006 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558709 | C2 | semidirect |
| 6. #22558111 | C2 | semidirect |
| 7. C67×#1478 | C2 | semidirect |
| 37. #14524043 | D4 | semidirect |
| 38. #14524043 | D4 | semidirect |
| 58. C4⋊(C67⋊C8) | D4 | semidirect |
| 73. C4⋊C8×C67 | D4 | semidirect |
| 119. C2×D4×C67 | SD16 | semidirect |
| 227. #1478 | D67 | semidirect |
| 229. C67 | #10246 | semidirect |
| 291. C4⋊C8 | C22⋊D67 | semidirect |
| 324. C2×D4 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571152 | 2 |
| #22570006 | 2 |
| #22565155 | 2 |
| #22558876 | 2 |
| #22558709 | 2 |
| #22558111 | 2 |
| C67×#1478 | 2 |
| #10246 | 67 |