Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 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. #21435014 | C2 | semidirect |
| 2. #21433560 | C2 | semidirect |
| 3. #21422764 | C2 | semidirect |
| 4. #21422590 | C2 | semidirect |
| 5. #21422487 | C2 | semidirect |
| 6. #21421999 | C2 | semidirect |
| 7. C59×#2541 | C2 | semidirect |
| 38. #14273727 | D4 | semidirect |
| 39. #14273724 | D4 | semidirect |
| 47. C4⋊(C59⋊C8) | D4 | semidirect |
| 48. C4⋊(C59⋊C8) | D4 | semidirect |
| 102. C2×D4×C59 | D8 | semidirect |
| 235. #2541 | D59 | semidirect |
| 271. C59 | #10238 | semidirect |
| 352. C2×D4 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435014 | 2 |
| #21433560 | 2 |
| #21422764 | 2 |
| #21422590 | 2 |
| #21422487 | 2 |
| #21421999 | 2 |
| C59×#2541 | 2 |
| #10238 | 59 |