Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
602 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21434127 | C2 | semidirect |
| 3. #21422655 | C2 | semidirect |
| 4. #21422525 | C2 | semidirect |
| 5. #21422487 | C2 | semidirect |
| 6. #21421954 | C2 | semidirect |
| 7. C59×#2580 | C2 | semidirect |
| 93. C2×D4×C59 | SD16 | semidirect |
| 228. #2580 | D59 | semidirect |
| 265. C59 | #9998 | semidirect |
| 335. C2×D4 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434127 | 2 |
| #21433560 | 2 |
| #21422655 | 2 |
| #21422525 | 2 |
| #21422487 | 2 |
| #21421954 | 2 |
| C59×#2580 | 2 |
| #9998 | 59 |