Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. #29505577 | C2 | semidirect |
| 2. #29505208 | C2 | semidirect |
| 3. C2×#21439901 | C2 | semidirect |
| 4. #29504584 | C2 | semidirect |
| 5. #29504578 | C2 | semidirect |
| 6. #29504556 | C2 | semidirect |
| 7. #472×C239 | C2 | semidirect |
| 18. #21439900 | C22 | semidirect |
| 19. C2×C239⋊C16 | C22 | semidirect |
| 21. C2×D8×C239 | C22 | semidirect |
| 23. #108×C239 | C22 | semidirect |
| 93. C239 | #2192 | semidirect |
| 98. #472 | D239 | semidirect |
| 110. C2×D8 | C2×D239 | semidirect |
| 117. #108 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505577 | 2 |
| #29505208 | 2 |
| C2×#21439901 | 2 |
| #29504584 | 2 |
| #29504578 | 2 |
| #29504556 | 2 |
| #472×C239 | 2 |
| #2192 | 239 |