Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22562114 | C2 | semidirect |
| 4. #22558272 | C2 | semidirect |
| 5. #22558189 | C2 | semidirect |
| 6. C16×C67⋊C8 | C2 | semidirect |
| 55. C67⋊C16 | SD16 | semidirect |
| 88. C67⋊C8 | M32 | semidirect |
| 113. C67 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562114 | 2 |
| #22562041 | 2 |
| C8×#11761616 | 2 |
| #22558272 | 2 |
| #22558189 | 2 |
| C16×C67⋊C8 | 2 |
| C67×D4⋊C16 | 2 |
| #12051 | 67 |