Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2118 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2118 conjugacy classes of subgroups — too many to draw. Only its 587 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. C22×#14273750 | C2 | semidirect |
| 2. C2×#16837835 | C2 | direct (N × H) |
| 3. C22×#14273670 | C2 | semidirect |
| 4. C22×D944 | C2 | semidirect |
| 5. C22×C16×D59 | C2 | semidirect |
| 6. C22×Q32×C59 | C2 | semidirect |
| 9. C2×#14273750 | C22 | semidirect |
| 13. #16837835 | C22 | direct (N × H) |
| 14. C2×#14273670 | C22 | semidirect |
| 15. C2×D944 | C22 | semidirect |
| 17. C2×C16×D59 | C22 | semidirect |
| 19. C2×Q32×C59 | C22 | semidirect |
| 28. #14273750 | C23 | semidirect |
| 35. #14273670 | C23 | semidirect |
| 36. D944 | C23 | semidirect |
| 38. C16×D59 | C23 | semidirect |
| 43. Q32×C59 | C23 | semidirect |
| 93. C22×C59 | #508 | semidirect |
| 105. C22×Q32 | D59 | semidirect |
| 109. C2×C59 | C2×#508 | semidirect |
| 121. C2×Q32 | C2×D59 | semidirect |
| 127. C59 | C22×#508 | semidirect |
| 146. Q32 | C22×D59 | semidirect |
| 203. C22 | #16837835 | direct (N × H) |
| 211. C2 | C2×#16837835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273750 | 2 |
| C2×#16837835 | 2 |
| C22×#14273670 | 2 |
| C22×D944 | 2 |
| C22×C16×D59 | 2 |
| C22×Q32×C59 | 2 |
| C22×#508 | 59 |