Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1030 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×#16840136 | C2 | semidirect |
| 3. C2×#16840110 | C2 | semidirect |
| 4. #21445448 | C2 | direct (N × H) |
| 5. C2×#16839483 | C2 | semidirect |
| 6. C2×C61×#498 | C2 | semidirect |
| 14. #16840136 | C22 | semidirect |
| 16. #16840110 | C22 | semidirect |
| 19. #16839483 | C22 | semidirect |
| 22. C61×#498 | C22 | semidirect |
| 75. C2×C8×C61 | SD16 | semidirect |
| 113. C8×C61 | C2×SD16 | semidirect |
| 130. C2×#498 | D61 | semidirect |
| 136. C2×C61 | #1715 | semidirect |
| 147. #498 | C2×D61 | semidirect |
| 159. C61 | C2×#1715 | semidirect |
| 214. C2×C8 | #11758201 | semidirect |
| 249. C8 | C2×#11758201 | semidirect |
| 266. C2 | #21445448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840139 | 2 |
| C2×#16840136 | 2 |
| C2×#16840110 | 2 |
| #21445448 | 2 |
| C2×#16839483 | 2 |
| C2×C61×#498 | 2 |
| C2×#1715 | 61 |