Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #107×D97 | C2 | semidirect |
| 3. #20260561 | C2 | semidirect |
| 4. #20260560 | C2 | semidirect |
| 5. #20260536 | C2 | semidirect |
| 6. #20260514 | C2 | semidirect |
| 7. #357×C97 | C2 | semidirect |
| 71. C97 | #2232 | semidirect |
| 77. #357 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260968 | 2 |
| #107×D97 | 2 |
| #20260561 | 2 |
| #20260560 | 2 |
| #20260536 | 2 |
| #20260514 | 2 |
| #357×C97 | 2 |
| #2232 | 97 |