Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #22558180 | C2 | semidirect |
| 5. #22558179 | C2 | semidirect |
| 6. #22558178 | C2 | semidirect |
| 7. C67×#1334 | C2 | semidirect |
| 31. Q16×D67 | C8 | semidirect |
| 159. #1334 | D67 | semidirect |
| 160. C67 | #11600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D67 | 2 |
| #22561802 | 2 |
| #22558954 | 2 |
| #22558180 | 2 |
| #22558179 | 2 |
| #22558178 | 2 |
| C67×#1334 | 2 |
| #11600 | 67 |