Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
226 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22559106 | C2 | semidirect |
| 4. #22558280 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 110. #1332 | D67 | semidirect |
| 113. C67 | #12074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523986 | 2 |
| #22559106 | 2 |
| #22559003 | 2 |
| #22558280 | 2 |
| #22558171 | 2 |
| #22558128 | 2 |
| C67×#1332 | 2 |
| #12074 | 67 |