Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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×#15690907 | C2 | semidirect |
| 2. C2×#15690906 | C2 | semidirect |
| 3. #20261838 | C2 | semidirect |
| 4. #20261832 | C2 | semidirect |
| 5. C22⋊#13095523 | C2 | semidirect |
| 6. C4×#13095523 | C2 | semidirect |
| 24. #13095523 | D4 | semidirect |
| 67. Dic97 | M32 | semidirect |
| 76. C97 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690907 | 2 |
| C2×#15690906 | 2 |
| #20261838 | 2 |
| #20261832 | 2 |
| C22⋊#13095523 | 2 |
| C4×#13095523 | 2 |
| #20261762 | 2 |
| #2169 | 97 |