Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 572 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. C22×#14273668 | C2 | semidirect |
| 2. C2×#16837669 | C2 | semidirect |
| 3. #21433745 | C2 | semidirect |
| 4. C2×#16837216 | C2 | semidirect |
| 5. C2×#16837187 | C2 | semidirect |
| 6. #21422191 | C2 | semidirect |
| 7. C59×#2140 | C2 | semidirect |
| 56. C2×C59⋊C16 | D4 | semidirect |
| 58. #14273663 | D4 | semidirect |
| 67. C2×D8×C59 | D4 | semidirect |
| 197. #2140 | D59 | semidirect |
| 228. C59 | #13319 | semidirect |
| 247. C2×D8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273668 | 2 |
| C2×#16837669 | 2 |
| #21433745 | 2 |
| C2×#16837216 | 2 |
| C2×#16837187 | 2 |
| #21422191 | 2 |
| C59×#2140 | 2 |
| #13319 | 59 |