Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
242 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 85 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. C16×D236 | C2 | semidirect |
| 3. #21422159 | C2 | semidirect |
| 4. D4⋊(C59⋊C16) | C2 | semidirect |
| 5. #21422050 | C2 | semidirect |
| 6. #21422015 | C2 | semidirect |
| 7. C59×#2169 | C2 | semidirect |
| 83. D236 | M32 | semidirect |
| 109. #2169 | D59 | semidirect |
| 136. C59 | #12063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D236 | 2 |
| C8×#11745669 | 2 |
| #21422159 | 2 |
| D4⋊(C59⋊C16) | 2 |
| #21422050 | 2 |
| #21422015 | 2 |
| C59×#2169 | 2 |
| #12063 | 59 |