Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1060 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. C2×#16837535 | C2 | semidirect |
| 2. #21427734 | C2 | semidirect |
| 3. #21424933 | C2 | semidirect |
| 4. #21424028 | C2 | semidirect |
| 5. #21422664 | C2 | semidirect |
| 6. #21421943 | C2 | semidirect |
| 7. C59×#3186 | C2 | semidirect |
| 55. C22⋊(C59⋊C8) | D4 | semidirect |
| 61. C22×D4×C59 | D4 | semidirect |
| 64. C22×C8×C59 | D4 | semidirect |
| 74. C2×C4⋊C4×C59 | D4 | semidirect |
| 146. C22⋊Dic59 | D8 | semidirect |
| 259. #3186 | D59 | semidirect |
| 299. C59 | #9946 | semidirect |
| 312. C22×D4 | C22⋊D59 | semidirect |
| 318. C22×C8 | C22⋊D59 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837535 | 2 |
| #21427734 | 2 |
| #21424933 | 2 |
| #21424028 | 2 |
| #21422664 | 2 |
| #21421943 | 2 |
| C59×#3186 | 2 |
| #9946 | 59 |