Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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. #21426349 | C2 | semidirect |
| 4. #21426348 | C2 | semidirect |
| 5. #21426347 | C2 | semidirect |
| 7. C59×#2247 | C2 | semidirect |
| 90. C4×D59 | Q32 | semidirect |
| 105. C4×C59 | C2×Q32 | semidirect |
| 110. Dic59 | C2×Q32 | semidirect |
| 116. #2247 | D59 | direct (N × H) |
| 120. D59 | #2247 | direct (N × H) |
| 138. C59 | C2×#2247 | semidirect |
| 221. C4 | Q32×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D59 | 2 |
| #494×D59 | 2 |
| #21426349 | 2 |
| #21426348 | 2 |
| #21426347 | 2 |
| C4×C16×D59 | 2 |
| C59×#2247 | 2 |
| C2×#2247 | 59 |