Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. #21422994 | C2 | semidirect |
| 4. #21422170 | C2 | semidirect |
| 5. #21422061 | C2 | semidirect |
| 7. C8×C16×C59 | C2 | semidirect |
| 67. C16×C59 | M16 | semidirect |
| 84. C8×C59 | SD32 | semidirect |
| 108. C8×C16 | D59 | semidirect |
| 128. C59 | #12082 | semidirect |
| 173. C16 | #11745659 | semidirect |
| 192. C8 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273672 | 2 |
| #21422994 | 2 |
| #21422982 | 2 |
| #21422170 | 2 |
| #21422061 | 2 |
| #21422058 | 2 |
| C8×C16×C59 | 2 |
| #12082 | 59 |