Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 17. #16863144 | C4 | semidirect |
| 18. #16863143 | C4 | semidirect |
| 146. C67 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561186 | 2 |
| C4×C4⋊(C67⋊C8) | 2 |
| #22558980 | 2 |
| #22558864 | 2 |
| #22558613 | 2 |
| #22558105 | 2 |
| C67×#1276 | 2 |
| #9579 | 67 |