Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
560 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 560 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. #22570014 | C2 | semidirect |
| 5. #22558613 | C2 | semidirect |
| 6. #22558105 | C2 | semidirect |
| 7. C67×#1461 | C2 | semidirect |
| 113. C2×Q8×C67 | SD16 | semidirect |
| 208. #1461 | D67 | semidirect |
| 210. C67 | #10179 | semidirect |
| 288. C2×Q8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571152 | 2 |
| #22570014 | 2 |
| C2×#16863596 | 2 |
| #22558876 | 2 |
| #22558613 | 2 |
| #22558105 | 2 |
| C67×#1461 | 2 |
| #10179 | 67 |