Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #22565571 | C2 | semidirect |
| 5. #22558639 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1479 | C2 | semidirect |
| 124. C2×Q8×C67 | SD16 | semidirect |
| 225. #1479 | D67 | semidirect |
| 227. C67 | #9999 | semidirect |
| 317. C2×Q8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570241 | 2 |
| #22569681 | 2 |
| #22565571 | 2 |
| #22558770 | 2 |
| #22558639 | 2 |
| #22558068 | 2 |
| C67×#1479 | 2 |
| #9999 | 67 |