Finite Group DatabasebetaFinite Group DatabasebetaOrder 19648.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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. #23754293 | C2 | semidirect |
| 3. #23754290 | C2 | semidirect |
| 4. #23754248 | C2 | semidirect |
| 5. #23754188 | C2 | semidirect |
| 6. #23754176 | C2 | semidirect |
| 7. #104×C307 | C2 | semidirect |
| 11. C2×Dic614 | C22 | semidirect |
| 20. #19096810 | C22 | semidirect |
| 23. M16×C307 | C22 | semidirect |
| 24. C42×C307 | C22 | semidirect |
| 64. C307 | #455 | semidirect |
| 71. #104 | D307 | semidirect |
| 87. M16 | C2×D307 | semidirect |
| 89. C42 | C2×D307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23754306 | 2 |
| #23754293 | 2 |
| #23754290 | 2 |
| #23754248 | 2 |
| #23754188 | 2 |
| #23754176 | 2 |
| #104×C307 | 2 |
| #455 | 307 |