Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #22558800 | C2 | semidirect |
| 3. #22558627 | C2 | semidirect |
| 4. C8×#11761612 | C2 | semidirect |
| 5. C4×#108×C67 | C2 | semidirect |
| 136. C4×#108 | D67 | semidirect |
| 140. C67 | #9724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22558800 | 2 |
| #22558627 | 2 |
| C8×#11761612 | 2 |
| C4×#108×C67 | 2 |
| #9724 | 67 |