Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 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×#15690840 | C2 | semidirect |
| 2. C2×#15690810 | C2 | semidirect |
| 3. #20261130 | C2 | semidirect |
| 4. #20261114 | C2 | semidirect |
| 5. #20261107 | C2 | semidirect |
| 6. C4×#13095495 | C2 | semidirect |
| 32. #13095495 | D4 | semidirect |
| 76. C4×C97 | #137 | semidirect |
| 84. C97 | #3152 | semidirect |
| 161. C4 | #15690840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690810 | 2 |
| #20261130 | 2 |
| #20261114 | 2 |
| #20261107 | 2 |
| C4×#13095495 | 2 |
| #532×C97 | 2 |
| #3152 | 97 |