Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690830 | C2 | semidirect |
| 2. #20261285 | C2 | semidirect |
| 3. #20261117 | C2 | semidirect |
| 4. #20261114 | C2 | semidirect |
| 5. #20261111 | C2 | semidirect |
| 6. #20261109 | C2 | semidirect |
| 7. #20261107 | C2 | semidirect |
| 8. C2×C4×#11715895 | C2 | semidirect |
| 9. #532×C97 | C2 | semidirect |
| 42. C2×#11715895 | D4 | semidirect |
| 93. C4×C97 | #135 | semidirect |
| 102. C97 | #3147 | semidirect |
| 105. #532 | D97 | semidirect |
| 196. C4 | #15690830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| #20261285 | 2 |
| #20261117 | 2 |
| #20261114 | 2 |
| #20261111 | 2 |
| #20261109 | 2 |
| #20261107 | 2 |
| C2×C4×#11715895 | 2 |
| #532×C97 | 2 |
| #3147 | 97 |