Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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×D944 | C2 | semidirect |
| 2. C22×#14273666 | C2 | semidirect |
| 3. C2×#16837639 | C2 | semidirect |
| 4. #21426200 | C2 | direct (N × H) |
| 5. C2×#16837202 | C2 | semidirect |
| 6. C2×C59×#367 | C2 | semidirect |
| 11. C2×D944 | C22 | semidirect |
| 13. C2×#14273666 | C22 | semidirect |
| 16. #16837639 | C22 | semidirect |
| 18. #16837202 | C22 | semidirect |
| 21. C59×#367 | C22 | semidirect |
| 44. C2×C16×C59 | D4 | semidirect |
| 78. C16×C59 | C2×D4 | semidirect |
| 127. C2×#367 | D59 | semidirect |
| 129. C2×C59 | #2218 | semidirect |
| 147. #367 | C2×D59 | semidirect |
| 149. C59 | C2×#2218 | semidirect |
| 171. C2×C16 | D236 | semidirect |
| 207. C16 | C2×D236 | semidirect |
| 252. C2 | #21426200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D944 | 2 |
| C22×#14273666 | 2 |
| C2×#16837639 | 2 |
| #21426200 | 2 |
| C2×#16837202 | 2 |
| C2×C59×#367 | 2 |
| C2×#2218 | 59 |