Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1910 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1910 conjugacy classes of subgroups — too many to draw. Only its 297 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. H(5,𝔽2)×Dic61 | C2 | semidirect |
| 2. #120×Dic61 | C2 | semidirect |
| 3. #21446228 | C2 | semidirect |
| 4. #21446102 | C2 | semidirect |
| 5. #21445767 | C2 | semidirect |
| 6. #99×Dic61 | C2 | semidirect |
| 8. C24×Dic61 | C22 | semidirect |
| 20. #16839637 | C22 | semidirect |
| 21. #16839618 | C22 | semidirect |
| 23. C22⋊C4×Dic61 | C22 | semidirect |
| 24. #16839528 | C22 | semidirect |
| 27. C61×B(4,𝔽2) | C4 | semidirect |
| 33. C23×Dic61 | D4 | semidirect |
| 50. C2×C4⋊Dic61 | D4 | semidirect |
| 56. C2×C22⋊Dic61 | D4 | semidirect |
| 61. C2×C4×Dic61 | D4 | semidirect |
| 68. H(5,𝔽2)×C61 | C2×C4 | semidirect |
| 74. #120×C61 | C2×C4 | semidirect |
| 77. #99×C61 | C2×C4 | semidirect |
| 83. C24×C61 | C22×C4 | semidirect |
| 124. C22⋊C4×C61 | C22×C4 | semidirect |
| 158. C23×C61 | C4×D4 | semidirect |
| 173. C2×C4×C61 | C4×D4 | semidirect |
| 222. Dic61 | B(4,𝔽2) | direct (N × H) |
| 247. B(4,𝔽2) | Dic61 | direct (N × H) |
| 258. C61 | C4×B(4,𝔽2) | semidirect |
| 261. H(5,𝔽2) | C2×Dic61 | semidirect |
| 274. #120 | C2×Dic61 | semidirect |
| 304. #99 | C2×Dic61 | semidirect |
| 314. C24 | C22×Dic61 | semidirect |
| 365. C22⋊C4 | C22×Dic61 | semidirect |
| 388. C23 | D4×Dic61 | semidirect |
| 423. C2×C4 | D4×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic61 | 2 |
| #120×Dic61 | 2 |
| #21446228 | 2 |
| #21446102 | 2 |
| #21445767 | 2 |
| #99×Dic61 | 2 |
| C2×C61×B(4,𝔽2) | 2 |
| C4×B(4,𝔽2) | 61 |