Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 297 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. D4×#11715895 | C2 | semidirect |
| 2. #20260788 | C2 | semidirect |
| 3. C2×C22⋊#11715895 | C2 | semidirect |
| 5. C22×#11715895 | C22 | semidirect |
| 6. C4⋊#11715895 | C22 | semidirect |
| 8. C22⋊#11715895 | C22 | semidirect |
| 9. C4×#11715895 | C22 | semidirect |
| 20. C2×D4×C97 | C8 | semidirect |
| 35. C23×C97 | C2×C8 | semidirect |
| 38. D4×C97 | C2×C8 | semidirect |
| 44. C2×C4×C97 | C2×C8 | semidirect |
| 70. C97 | #2972 | semidirect |
| 88. C2×D4 | #11715895 | semidirect |
| 105. C23 | C2×#11715895 | semidirect |
| 108. D4 | C2×#11715895 | semidirect |
| 114. C2×C4 | C2×#11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11715895 | 2 |
| #20260788 | 2 |
| C2×C22⋊#11715895 | 2 |
| C2×C4×D4×C97 | 2 |
| #2972 | 97 |