Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16837524 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. #21424970 | C2 | semidirect |
| 5. #21422194 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C2×C59×#360 | C2 | semidirect |
| 12. C2×#14273670 | C4 | semidirect |
| 13. C2×#14273668 | C4 | semidirect |
| 87. Q16×C59 | C22⋊C4 | semidirect |
| 91. D8×C59 | C22⋊C4 | semidirect |
| 175. C2×#360 | D59 | semidirect |
| 204. C59 | #13040 | semidirect |
| 265. Q16 | (C2×D59)⋊C4 | semidirect |
| 273. D8 | (C2×D59)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| C2×#16837524 | 2 |
| C2×#16837216 | 2 |
| #21424970 | 2 |
| #21422194 | 2 |
| #21422175 | 2 |
| C2×C59×#360 | 2 |
| #13040 | 59 |