Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22559028 | C2 | semidirect |
| 3. #22558275 | C2 | semidirect |
| 4. #22558179 | C2 | semidirect |
| 6. #22558129 | C2 | semidirect |
| 36. SD32×C67 | C8 | semidirect |
| 54. Q16×C67 | C2×C8 | semidirect |
| 66. C16×C67 | C2×C8 | semidirect |
| 110. C67 | #12065 | semidirect |
| 131. SD32 | C67⋊C8 | semidirect |
| 151. Q16 | C2×C67⋊C8 | semidirect |
| 169. C16 | C2×C67⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22559033 | 2 |
| #22559028 | 2 |
| #22558275 | 2 |
| #22558179 | 2 |
| #22558176 | 2 |
| #22558129 | 2 |
| C67×#2175 | 2 |
| #12065 | 67 |