Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16837838 | C2 | semidirect |
| 2. #21433817 | C2 | semidirect |
| 3. #21433740 | C2 | semidirect |
| 4. #21425833 | C2 | semidirect |
| 5. #21425723 | C2 | semidirect |
| 6. #21422210 | C2 | semidirect |
| 7. C2×C59×#361 | C2 | semidirect |
| 42. C2×Dic236 | D4 | semidirect |
| 44. C2×D472 | D4 | semidirect |
| 60. #14273667 | D4 | semidirect |
| 80. #108×C59 | D4 | semidirect |
| 208. C2×#361 | D59 | semidirect |
| 242. C59 | #13310 | semidirect |
| 287. #108 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21433817 | 2 |
| #21433740 | 2 |
| #21425833 | 2 |
| #21425723 | 2 |
| #21422210 | 2 |
| C2×C59×#361 | 2 |
| #13310 | 59 |