Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21437246 | C2 | semidirect |
| 2. #21426408 | C2 | semidirect |
| 3. C2×#16837241 | C2 | semidirect |
| 4. #21426217 | C2 | semidirect |
| 5. #21422288 | C2 | semidirect |
| 6. #21422237 | C2 | semidirect |
| 7. C59×#1417 | C2 | semidirect |
| 119. #1417 | D59 | semidirect |
| 143. C59 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437246 | 2 |
| #21426408 | 2 |
| C2×#16837241 | 2 |
| #21426217 | 2 |
| #21422288 | 2 |
| #21422237 | 2 |
| C59×#1417 | 2 |
| #13670 | 59 |