Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
330 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #21426323 | C2 | semidirect |
| 3. #21426138 | C2 | semidirect |
| 4. #21422152 | C2 | semidirect |
| 5. #21422056 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 7. C59×#1669 | C2 | semidirect |
| 92. D4×C59 | SD32 | semidirect |
| 135. #1669 | D59 | semidirect |
| 161. C59 | #12344 | semidirect |
| 234. D4 | #14273670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436444 | 2 |
| #21426323 | 2 |
| #21426138 | 2 |
| #21422152 | 2 |
| #21422056 | 2 |
| D4⋊(C59⋊C16) | 2 |
| C59×#1669 | 2 |
| #12344 | 59 |