Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. #21461757 | C2 | semidirect |
| 4. #21461742 | C2 | semidirect |
| 5. #21460696 | C2 | semidirect |
| 6. #21460696 | C2 | semidirect |
| 27. #16839502 | C4 | semidirect |
| 28. #16839501 | C4 | semidirect |
| 29. #16839501 | C4 | semidirect |
| 30. C61×#329 | C4 | semidirect |
| 69. #14519688 | C2×C4 | semidirect |
| 70. #14519688 | C2×C4 | semidirect |
| 74. #97×C61 | C2×C4 | semidirect |
| 75. #97×C61 | C2×C4 | semidirect |
| 257. #329 | #6923 | semidirect |
| 258. C61 | #8911 | semidirect |
| 296. #97 | C2×#6923 | semidirect |
| 297. #97 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462362 | 2 |
| #21461949 | 2 |
| #21461757 | 2 |
| #21461742 | 2 |
| #21460696 | 2 |
| #329×D61 | 2 |
| #8911 | 61 |