Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16837837 | C2 | semidirect |
| 2. #21434583 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21425813 | C2 | semidirect |
| 5. #21424995 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 7. C59×#3414 | C2 | semidirect |
| 54. #14273667 | D4 | semidirect |
| 73. C2×Q16×C59 | D4 | semidirect |
| 77. C2×D8×C59 | D4 | semidirect |
| 85. C2×C16×C59 | D4 | semidirect |
| 211. #3414 | D59 | semidirect |
| 250. C59 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D59 | semidirect |
| 277. C2×D8 | C22⋊D59 | semidirect |
| 297. C2×C16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| #21434583 | 2 |
| #21425832 | 2 |
| #21425813 | 2 |
| #21424995 | 2 |
| #21422181 | 2 |
| C59×#3414 | 2 |
| #13334 | 59 |