Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425897 | C2 | semidirect |
| 3. #21422850 | C2 | semidirect |
| 4. #21422066 | C2 | semidirect |
| 5. #21422064 | C2 | semidirect |
| 6. #21422062 | C2 | semidirect |
| 7. C59×#1334 | C2 | semidirect |
| 74. Q16×C59 | M16 | semidirect |
| 97. D472 | M16 | semidirect |
| 156. #1334 | D59 | semidirect |
| 183. C59 | #11666 | semidirect |
| 231. Q16 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273750 | 2 |
| #21425897 | 2 |
| #21422850 | 2 |
| #21422066 | 2 |
| #21422064 | 2 |
| #21422062 | 2 |
| C59×#1334 | 2 |
| #11666 | 59 |