Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 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. #21437230 | C2 | semidirect |
| 2. #21434539 | C2 | semidirect |
| 3. #21425825 | C2 | semidirect |
| 4. #21425824 | C2 | semidirect |
| 5. #21424990 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C59×#3414 | C2 | semidirect |
| 64. C2×C59⋊C16 | D4 | semidirect |
| 82. C2×Q16×C59 | D4 | semidirect |
| 86. C2×D8×C59 | D4 | semidirect |
| 94. C2×C16×C59 | D4 | semidirect |
| 229. #3414 | D59 | semidirect |
| 269. C59 | #13340 | semidirect |
| 290. C2×Q16 | C22⋊D59 | semidirect |
| 299. C2×D8 | C22⋊D59 | semidirect |
| 323. C2×C16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #21434539 | 2 |
| #21425825 | 2 |
| #21425824 | 2 |
| #21424990 | 2 |
| #21422175 | 2 |
| C59×#3414 | 2 |
| #13340 | 59 |