Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21437198 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. #21424143 | C2 | semidirect |
| 6. #21422212 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 47. #14273667 | D4 | semidirect |
| 60. M32×C59 | D4 | semidirect |
| 169. #1389 | D59 | semidirect |
| 194. C59 | #13079 | semidirect |
| 222. M32 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437198 | 2 |
| #21433745 | 2 |
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| #21424143 | 2 |
| #21422212 | 2 |
| C59×#1389 | 2 |
| #13079 | 59 |