Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×C22⋊#11715895 | C2 | semidirect |
| 2. #20260461 | C2 | semidirect |
| 3. #20260459 | C2 | semidirect |
| 23. C2×D4×C97 | C8 | semidirect |
| 48. C23×C97 | C2×C8 | semidirect |
| 66. C2×C4×C97 | C2×C8 | semidirect |
| 98. C97 | #1459 | semidirect |
| 119. C2×D4 | #11715895 | semidirect |
| 146. C23 | C2×#11715895 | semidirect |
| 164. C2×C4 | C2×#11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715895 | 2 |
| #20260461 | 2 |
| #20260459 | 2 |
| C2×C4×D4×C97 | 2 |
| #1459 | 97 |