Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #29504667 | C2 | semidirect |
| 3. #29504666 | C2 | semidirect |
| 4. #29504660 | C2 | semidirect |
| 5. #29504656 | C2 | semidirect |
| 7. #29504644 | C2 | semidirect |
| 8. #29504630 | C2 | semidirect |
| 12. #21439941 | C4 | semidirect |
| 36. C22×Dic239 | C2×C4 | semidirect |
| 44. Dic239⋊C4 | C2×C4 | semidirect |
| 48. C22⋊Dic239 | C2×C4 | semidirect |
| 126. C239 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439941 | 2 |
| #29504667 | 2 |
| #29504666 | 2 |
| #29504660 | 2 |
| #29504656 | 2 |
| #29504652 | 2 |
| #29504644 | 2 |
| #29504630 | 2 |
| #390×C239 | 2 |
| #2376 | 239 |