Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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×#14273721 | C2 | semidirect |
| 2. #21432170 | C2 | direct (N × H) |
| 3. C2×#16837332 | C2 | semidirect |
| 4. C2×#16837324 | C2 | semidirect |
| 6. C2×C59×#384 | C2 | semidirect |
| 9. C2×#14273721 | C22 | semidirect |
| 14. #16837332 | C22 | semidirect |
| 15. #16837324 | C22 | semidirect |
| 22. C59×#384 | C22 | semidirect |
| 45. C2×C42×C59 | D4 | semidirect |
| 69. C42×C59 | C2×D4 | semidirect |
| 118. C2×#384 | D59 | semidirect |
| 119. C2×C59 | #2823 | semidirect |
| 137. #384 | C2×D59 | semidirect |
| 140. C59 | C2×#2823 | semidirect |
| 161. C2×C42 | D236 | semidirect |
| 191. C42 | C2×D236 | semidirect |
| 231. C2 | #21432170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273721 | 2 |
| #21432170 | 2 |
| C2×#16837332 | 2 |
| C2×#16837324 | 2 |
| C2×#16837319 | 2 |
| C2×C59×#384 | 2 |
| C2×#2823 | 59 |