Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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 |
|---|---|---|
| 2. C23×#11715895 | C2 | semidirect |
| 3. C2×#15690730 | C2 | direct (N × H) |
| 4. C22×C4⋊C4×C97 | C2 | semidirect |
| 8. C22×D388 | C4 | semidirect |
| 11. C22×#11715895 | C22 | semidirect |
| 12. #15690730 | C22 | direct (N × H) |
| 16. C2×C4⋊C4×C97 | C22 | semidirect |
| 24. C2×D388 | C2×C4 | semidirect |
| 27. C2×#11715895 | C23 | semidirect |
| 36. C4⋊C4×C97 | C23 | semidirect |
| 55. D388 | C22×C4 | semidirect |
| 57. C22×C97 | #102 | semidirect |
| 70. C2×C97 | C2×#102 | semidirect |
| 76. C97 | C22×#102 | semidirect |
| 79. C22×C4⋊C4 | D97 | semidirect |
| 91. C2×C4⋊C4 | C2×D97 | semidirect |
| 112. C4⋊C4 | C22×D97 | semidirect |
| 137. C22 | #15690730 | direct (N × H) |
| 147. C2 | C2×#15690730 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C23×#11715895 | 2 |
| C2×#15690730 | 2 |
| C22×C4⋊C4×C97 | 2 |
| C22×#102 | 97 |