Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2398 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 2398 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 |
|---|---|---|
| 2. C2×#16837800 | C2 | direct (N × H) |
| 10. #16837800 | C22 | direct (N × H) |
| 26. C22×C8×C59 | Q8 | semidirect |
| 41. C2×C8×C59 | C2×Q8 | semidirect |
| 60. C8×C59 | C22×Q8 | semidirect |
| 62. C22×C59 | #498 | semidirect |
| 74. C2×C59 | C2×#498 | semidirect |
| 87. C59 | C22×#498 | semidirect |
| 93. C22×C8 | Dic118 | semidirect |
| 114. C2×C8 | C2×Dic118 | semidirect |
| 133. C8 | C22×Dic118 | semidirect |
| 134. C22 | #16837800 | direct (N × H) |
| 142. C2 | C2×#16837800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273727 | 2 |
| C2×#16837800 | 2 |
| C22×#14273659 | 2 |
| C22×C4×C8×C59 | 2 |
| C22×#498 | 59 |