Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
994 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 283 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. C2×#16840158 | C2 | semidirect |
| 4. #21445407 | C2 | direct (N × H) |
| 5. C2×C8×#92418 | C2 | semidirect |
| 6. C2×C61×#498 | C2 | semidirect |
| 12. #16840158 | C22 | semidirect |
| 19. C8×#92418 | C22 | semidirect |
| 22. C61×#498 | C22 | semidirect |
| 72. C2×C8×C61 | SD16 | semidirect |
| 84. C2×#92418 | SD16 | semidirect |
| 109. C8×C61 | C2×SD16 | semidirect |
| 110. #92418 | C2×SD16 | semidirect |
| 125. C2×#498 | D61 | semidirect |
| 130. C2×C61 | #1705 | semidirect |
| 142. #498 | C2×D61 | semidirect |
| 152. C61 | C2×#1705 | semidirect |
| 204. C2×C8 | #11758201 | semidirect |
| 238. C8 | C2×#11758201 | semidirect |
| 252. C2 | #21445407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840158 | 2 |
| C2×#16840136 | 2 |
| C2×#16840135 | 2 |
| #21445407 | 2 |
| C2×C8×#92418 | 2 |
| C2×C61×#498 | 2 |
| C2×#1705 | 61 |