Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
412 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 164 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. #20261785 | C2 | semidirect |
| 2. #20261770 | C2 | semidirect |
| 3. #20261767 | C2 | semidirect |
| 4. #20261754 | C2 | semidirect |
| 5. #20261751 | C2 | semidirect |
| 6. C4×#13095520 | C2 | semidirect |
| 7. C4×#13095519 | C2 | semidirect |
| 78. C4×D97 | M16 | semidirect |
| 82. #11715897 | #41 | semidirect |
| 105. C97 | #2965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261785 | 2 |
| #20261770 | 2 |
| #20261767 | 2 |
| #20261754 | 2 |
| #20261751 | 2 |
| C4×#13095520 | 2 |
| C4×#13095519 | 2 |
| C4×#13095510 | 2 |
| #2965 | 97 |