Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
662 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21434564 | C2 | semidirect |
| 2. #21434183 | C2 | semidirect |
| 3. #21429951 | C2 | semidirect |
| 4. #21422719 | C2 | semidirect |
| 5. #21422538 | C2 | semidirect |
| 6. #21421960 | C2 | semidirect |
| 7. C59×#1514 | C2 | semidirect |
| 66. #14273638 | D4 | semidirect |
| 67. C4×C59⋊C8 | D4 | semidirect |
| 70. C4⋊Q8×C59 | D4 | semidirect |
| 71. #127×C59 | D4 | semidirect |
| 225. #1514 | D59 | semidirect |
| 260. C59 | #10018 | semidirect |
| 275. C4⋊Q8 | D236 | semidirect |
| 276. #127 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434564 | 2 |
| #21434183 | 2 |
| #21429951 | 2 |
| #21422719 | 2 |
| #21422538 | 2 |
| #21421960 | 2 |
| C59×#1514 | 2 |
| #10018 | 59 |