Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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. C23×#11715895 | C2 | semidirect |
| 2. C22×C4⋊Dic97 | C2 | semidirect |
| 3. C2×#15690731 | C2 | direct (N × H) |
| 7. C22×#11715895 | C22 | semidirect |
| 9. C2×C4⋊Dic97 | C22 | semidirect |
| 10. #15690731 | C22 | direct (N × H) |
| 14. C22×D4×C97 | C4 | semidirect |
| 20. C2×#11715895 | C23 | semidirect |
| 22. C4⋊Dic97 | C23 | semidirect |
| 31. C2×D4×C97 | C2×C4 | semidirect |
| 48. D4×C97 | C22×C4 | semidirect |
| 61. C22×C97 | #102 | semidirect |
| 71. C2×C97 | C2×#102 | semidirect |
| 76. C97 | C22×#102 | semidirect |
| 84. C22×D4 | Dic97 | semidirect |
| 101. C2×D4 | C2×Dic97 | semidirect |
| 124. D4 | C22×Dic97 | semidirect |
| 137. C22 | #15690731 | direct (N × H) |
| 147. C2 | C2×#15690731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715895 | 2 |
| C22×C4⋊Dic97 | 2 |
| C2×#15690731 | 2 |
| C23×D4×C97 | 2 |
| C22×#102 | 97 |