Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
918 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 267 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. C22×#14273672 | C2 | semidirect |
| 2. C2×#16837782 | C2 | semidirect |
| 4. #21426352 | C2 | direct (N × H) |
| 5. C2×C4×C16×C59 | C2 | semidirect |
| 13. C2×#14273672 | C22 | semidirect |
| 15. #16837782 | C22 | semidirect |
| 20. C4×C16×C59 | C22 | semidirect |
| 43. C2×C16×C59 | D4 | semidirect |
| 75. C16×C59 | C2×D4 | semidirect |
| 80. C2×C4×C59 | SD32 | semidirect |
| 106. C4×C59 | C2×SD32 | semidirect |
| 114. C2×C4×C16 | D59 | semidirect |
| 115. C2×C59 | #2248 | semidirect |
| 133. C4×C16 | C2×D59 | semidirect |
| 134. C59 | C2×#2248 | semidirect |
| 157. C2×C16 | D236 | semidirect |
| 189. C16 | C2×D236 | semidirect |
| 203. C2×C4 | #14273672 | semidirect |
| 220. C4 | C2×#14273672 | semidirect |
| 224. C2 | #21426352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273672 | 2 |
| C2×#16837782 | 2 |
| C2×#16837779 | 2 |
| #21426352 | 2 |
| C2×C4×C16×C59 | 2 |
| C2×#2248 | 59 |