Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20261138 | C2 | semidirect |
| 3. #20261109 | C2 | semidirect |
| 4. #20261107 | C2 | semidirect |
| 5. #20261082 | C2 | semidirect |
| 6. C8×#11715895 | C2 | semidirect |
| 7. #486×C97 | C2 | semidirect |
| 56. #11715895 | D8 | semidirect |
| 57. #11715895 | SD16 | semidirect |
| 76. C97 | #1706 | semidirect |
| 82. #486 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261138 | 2 |
| #20261111 | 2 |
| #20261109 | 2 |
| #20261107 | 2 |
| #20261082 | 2 |
| C8×#11715895 | 2 |
| #486×C97 | 2 |
| #1706 | 97 |