Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
908 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 191 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. #21433000 | C2 | semidirect |
| 2. #21432801 | C2 | semidirect |
| 3. #21425650 | C2 | semidirect |
| 4. #21425613 | C2 | semidirect |
| 5. #21425201 | C2 | semidirect |
| 6. #21425164 | C2 | semidirect |
| 7. C59×#1747 | C2 | semidirect |
| 50. #97×C59 | D4 | semidirect |
| 51. C4×C8×C59 | D4 | semidirect |
| 126. #1747 | D59 | semidirect |
| 147. C59 | #23795 | semidirect |
| 174. #97 | D236 | semidirect |
| 175. C4×C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433000 | 2 |
| #21432801 | 2 |
| #21425650 | 2 |
| #21425613 | 2 |
| #21425201 | 2 |
| #21425164 | 2 |
| C59×#1747 | 2 |
| #23795 | 59 |