Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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. #20261770 | C2 | semidirect |
| 2. #20261769 | C2 | semidirect |
| 3. #20261597 | C2 | semidirect |
| 4. #20261583 | C2 | semidirect |
| 5. D4⋊#11715897 | C2 | semidirect |
| 6. #20261576 | C2 | semidirect |
| 63. #11715895 | M16 | semidirect |
| 84. C97 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261770 | 2 |
| #20261769 | 2 |
| #20261597 | 2 |
| #20261583 | 2 |
| D4⋊#11715897 | 2 |
| #20261576 | 2 |
| #20260815 | 2 |
| #1594 | 97 |