Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20261137 | C2 | semidirect |
| 2. #20260562 | C2 | semidirect |
| 3. #20260560 | C2 | semidirect |
| 4. C4⋊#13095486 | C2 | semidirect |
| 63. C97 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261137 | 2 |
| #20260562 | 2 |
| #20260560 | 2 |
| C4⋊#13095486 | 2 |
| #20260536 | 2 |
| C4×D8×C97 | 2 |
| #2228 | 97 |