Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2078 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2078 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 |
|---|---|---|
| 2. C22×#14273673 | C2 | direct (N × H) |
| 8. C2×#14273673 | C22 | direct (N × H) |
| 19. #14273673 | C23 | direct (N × H) |
| 45. C23×C59 | Q32 | semidirect |
| 58. C22×C59 | C2×Q32 | semidirect |
| 68. C2×C59 | C22×Q32 | semidirect |
| 79. C59 | C23×Q32 | semidirect |
| 111. C23 | #14273673 | direct (N × H) |
| 123. C22 | C2×#14273673 | direct (N × H) |
| 129. C2 | C22×#14273673 | 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 |
| C22×#14273673 | 2 |
| C23×C59⋊C16 | 2 |
| C23×Q16×C59 | 2 |
| C23×Q32 | 59 |