Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21433889 | C2 | semidirect |
| 3. #21422660 | C2 | semidirect |
| 4. #21422521 | C2 | semidirect |
| 5. #21422488 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#3101 | C2 | semidirect |
| 52. C4⋊(C59⋊C8) | D4 | semidirect |
| 63. C4⋊Q8×C59 | D4 | semidirect |
| 64. C4⋊Q8×C59 | D4 | semidirect |
| 83. C4×C8×C59 | D4 | semidirect |
| 111. C2×D236 | SD16 | semidirect |
| 231. #3101 | D59 | semidirect |
| 270. C59 | #10000 | semidirect |
| 278. C4⋊Q8 | C22⋊D59 | semidirect |
| 279. C4⋊Q8 | C22⋊D59 | semidirect |
| 318. C4×C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433889 | 2 |
| #21428997 | 2 |
| #21422660 | 2 |
| #21422521 | 2 |
| #21422488 | 2 |
| #21421955 | 2 |
| C59×#3101 | 2 |
| #10000 | 59 |