Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
216 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22558275 | C2 | semidirect |
| 4. #22558274 | C2 | semidirect |
| 5. C67×#1368 | C2 | semidirect |
| 83. #1368 | D67 | semidirect |
| 84. C67 | #12021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561802 | 2 |
| #22558969 | 2 |
| #22558275 | 2 |
| #22558274 | 2 |
| C67×#1368 | 2 |
| #12021 | 67 |