Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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. #22560326 | C2 | semidirect |
| 4. #22558899 | C2 | semidirect |
| 6. #22558083 | C2 | semidirect |
| 7. C67×#1994 | C2 | semidirect |
| 114. C42×C67 | SD16 | semidirect |
| 191. #1994 | D67 | semidirect |
| 197. C67 | #10521 | semidirect |
| 304. C42 | #11761615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571521 | 2 |
| #22561037 | 2 |
| #22560326 | 2 |
| #22558899 | 2 |
| #22558887 | 2 |
| #22558083 | 2 |
| C67×#1994 | 2 |
| #10521 | 67 |