Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
246 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558131 | C2 | semidirect |
| 5. #22558130 | C2 | semidirect |
| 6. #22558129 | C2 | semidirect |
| 7. C67×#1313 | C2 | semidirect |
| 106. #1313 | D67 | semidirect |
| 107. C67 | #11415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562010 | 2 |
| #322×D67 | 2 |
| #22558131 | 2 |
| #22558130 | 2 |
| #22558129 | 2 |
| C67×#1313 | 2 |
| #11415 | 67 |