Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21434183 | C2 | semidirect |
| 2. #21429036 | C2 | semidirect |
| 3. #21425016 | C2 | semidirect |
| 4. #21422694 | C2 | semidirect |
| 5. #21422538 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#3213 | C2 | semidirect |
| 58. #14273638 | D4 | semidirect |
| 66. C4⋊Q8×C59 | D4 | semidirect |
| 67. #127×C59 | D4 | semidirect |
| 80. C4⋊C8×C59 | D4 | semidirect |
| 231. #3213 | D59 | semidirect |
| 271. C59 | #10004 | semidirect |
| 282. C4⋊Q8 | C22⋊D59 | semidirect |
| 283. #127 | C22⋊D59 | semidirect |
| 311. C4⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434183 | 2 |
| #21429036 | 2 |
| #21425016 | 2 |
| #21422694 | 2 |
| #21422538 | 2 |
| #21421953 | 2 |
| C59×#3213 | 2 |
| #10004 | 59 |