Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21434483 | C2 | semidirect |
| 2. #21434195 | C2 | semidirect |
| 4. #21422719 | C2 | semidirect |
| 5. #21422648 | C2 | semidirect |
| 6. #21421961 | C2 | semidirect |
| 7. C59×#1490 | C2 | semidirect |
| 37. #14273727 | D4 | semidirect |
| 38. #14273727 | D4 | semidirect |
| 62. #14273638 | D4 | semidirect |
| 81. C4×C8×C59 | D4 | semidirect |
| 210. #1490 | D59 | semidirect |
| 243. C59 | #10022 | semidirect |
| 288. C4×C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434483 | 2 |
| #21434195 | 2 |
| #21429948 | 2 |
| #21422719 | 2 |
| #21422648 | 2 |
| #21421961 | 2 |
| C59×#1490 | 2 |
| #10022 | 59 |