Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2334 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 747 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. C23×Dic236 | C2 | semidirect |
| 3. C22×#14273672 | C2 | direct (N × H) |
| 4. C23×C16×C59 | C2 | semidirect |
| 8. C22×Dic236 | C22 | semidirect |
| 11. C2×#14273672 | C22 | direct (N × H) |
| 13. C22×C16×C59 | C22 | semidirect |
| 21. C2×Dic236 | C23 | semidirect |
| 24. #14273672 | C23 | direct (N × H) |
| 28. C2×C16×C59 | C23 | semidirect |
| 42. Dic236 | C24 | semidirect |
| 45. C16×C59 | C24 | semidirect |
| 46. C23×C59 | SD32 | semidirect |
| 60. C22×C59 | C2×SD32 | semidirect |
| 70. C23×C16 | D59 | semidirect |
| 71. C2×C59 | C22×SD32 | semidirect |
| 82. C22×C16 | C2×D59 | semidirect |
| 83. C59 | C23×SD32 | semidirect |
| 98. C2×C16 | C22×D59 | semidirect |
| 115. C16 | C23×D59 | semidirect |
| 118. C23 | #14273672 | direct (N × H) |
| 131. C22 | C2×#14273672 | direct (N × H) |
| 137. C2 | C22×#14273672 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic236 | 2 |
| C23×D472 | 2 |
| C22×#14273672 | 2 |
| C23×C16×C59 | 2 |
| C23×SD32 | 59 |