Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21434100 | C2 | semidirect |
| 3. #21422660 | C2 | semidirect |
| 4. #21422520 | C2 | semidirect |
| 5. #21422487 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#3077 | C2 | semidirect |
| 56. C4×C59⋊C8 | D4 | semidirect |
| 63. C4⋊Q8×C59 | D4 | semidirect |
| 64. C4⋊Q8×C59 | D4 | semidirect |
| 81. C4⋊C8×C59 | D4 | semidirect |
| 93. C2×D4×C59 | SD16 | semidirect |
| 232. #3077 | D59 | semidirect |
| 270. C59 | #10000 | semidirect |
| 278. C4⋊Q8 | C22⋊D59 | semidirect |
| 279. C4⋊Q8 | C22⋊D59 | semidirect |
| 310. C4⋊C8 | C22⋊D59 | semidirect |
| 337. C2×D4 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434100 | 2 |
| #21428993 | 2 |
| #21422660 | 2 |
| #21422520 | 2 |
| #21422487 | 2 |
| #21421956 | 2 |
| C59×#3077 | 2 |
| #10000 | 59 |