Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
562 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21435021 | C2 | semidirect |
| 3. #21422781 | C2 | semidirect |
| 4. #21422494 | C2 | semidirect |
| 5. #21422417 | C2 | semidirect |
| 6. #21421993 | C2 | semidirect |
| 7. C2×C59×#476 | C2 | semidirect |
| 86. C2×D4×C59 | SD16 | semidirect |
| 204. C2×#476 | D59 | semidirect |
| 240. C59 | #10180 | semidirect |
| 305. C2×D4 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435021 | 2 |
| #21433560 | 2 |
| #21422781 | 2 |
| #21422494 | 2 |
| #21422417 | 2 |
| #21421993 | 2 |
| C2×C59×#476 | 2 |
| #10180 | 59 |