Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3262 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 3262 conjugacy classes of subgroups — too many to draw. Only its 1067 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 |
|---|---|---|
| 3. C2×#16837782 | C2 | direct (N × H) |
| 11. #16837782 | C22 | direct (N × H) |
| 32. C22×C4×C59 | Q16 | semidirect |
| 53. C2×C4×C59 | C2×Q16 | semidirect |
| 64. C22×C59 | #494 | semidirect |
| 69. C4×C59 | C22×Q16 | semidirect |
| 76. C2×C59 | C2×#494 | semidirect |
| 89. C59 | C22×#494 | semidirect |
| 113. C22×C4 | Dic236 | semidirect |
| 132. C2×C4 | C2×Dic236 | semidirect |
| 138. C22 | #16837782 | direct (N × H) |
| 144. C4 | C22×Dic236 | semidirect |
| 146. C2 | C2×#16837782 | 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×#14273727 | 2 |
| C2×#16837782 | 2 |
| C22×C4×C8×C59 | 2 |
| C22×#494 | 59 |