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×#14273746 | C2 | semidirect |
| 2. C2×#16837831 | C2 | direct (N × H) |
| 3. C22×Dic472 | C2 | semidirect |
| 4. C22×#14273671 | C2 | semidirect |
| 5. C22×C16×D59 | C2 | semidirect |
| 6. C22×D16×C59 | C2 | semidirect |
| 9. C2×#14273746 | C22 | semidirect |
| 13. #16837831 | C22 | direct (N × H) |
| 14. C2×Dic472 | C22 | semidirect |
| 15. C2×#14273671 | C22 | semidirect |
| 17. C2×C16×D59 | C22 | semidirect |
| 19. C2×D16×C59 | C22 | semidirect |
| 28. #14273746 | C23 | semidirect |
| 35. Dic472 | C23 | semidirect |
| 36. #14273671 | C23 | semidirect |
| 38. C16×D59 | C23 | semidirect |
| 43. D16×C59 | C23 | semidirect |
| 95. C22×C59 | #508 | semidirect |
| 107. C22×D16 | D59 | semidirect |
| 110. C2×C59 | C2×#508 | semidirect |
| 123. C2×D16 | C2×D59 | semidirect |
| 127. C59 | C22×#508 | semidirect |
| 148. D16 | C22×D59 | semidirect |
| 203. C22 | #16837831 | direct (N × H) |
| 211. C2 | C2×#16837831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273746 | 2 |
| C2×#16837831 | 2 |
| C22×Dic472 | 2 |
| C22×#14273671 | 2 |
| C22×C16×D59 | 2 |
| C22×D16×C59 | 2 |
| C22×#508 | 59 |