Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690833 | C2 | semidirect |
| 2. C2×#15690831 | C2 | semidirect |
| 3. C2×#15690829 | C2 | semidirect |
| 4. #20261284 | C2 | semidirect |
| 5. #20261119 | C2 | semidirect |
| 6. #20261117 | C2 | semidirect |
| 7. #20261113 | C2 | semidirect |
| 8. #20261110 | C2 | semidirect |
| 9. #20261106 | C2 | semidirect |
| 10. C4×C8×D97 | C2 | semidirect |
| 11. #495×C97 | C2 | semidirect |
| 62. C8×D97 | D4 | semidirect |
| 63. C8×D97 | D4 | semidirect |
| 119. Dic97 | #135 | semidirect |
| 126. C97 | #3147 | semidirect |
| 133. #495 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| C2×#15690831 | 2 |
| C2×#15690829 | 2 |
| #20261284 | 2 |
| #20261119 | 2 |
| #20261117 | 2 |
| #20261113 | 2 |
| #20261110 | 2 |
| #20261106 | 2 |
| C4×C8×D97 | 2 |
| #495×C97 | 2 |
| #3147 | 97 |