Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
242 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425928 | C2 | semidirect |
| 2. #21425915 | C2 | semidirect |
| 4. #21422159 | C2 | semidirect |
| 5. #21422052 | C2 | semidirect |
| 6. #21422015 | C2 | semidirect |
| 7. C59×D4⋊C16 | C2 | semidirect |
| 83. D236 | M32 | semidirect |
| 114. D4⋊C16 | 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 |
|---|---|
| #21425928 | 2 |
| #21425915 | 2 |
| C8×#11745669 | 2 |
| #21422159 | 2 |
| #21422052 | 2 |
| #21422015 | 2 |
| C59×D4⋊C16 | 2 |
| #12063 | 59 |