Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13095498 | C2 | semidirect |
| 2. C22×#13095496 | C2 | semidirect |
| 3. C2×#15690807 | C2 | semidirect |
| 4. #20261125 | C2 | direct (N × H) |
| 5. C2×#15690721 | C2 | semidirect |
| 6. C2×#124×C97 | C2 | semidirect |
| 10. C2×#13095498 | C22 | semidirect |
| 12. C2×#13095496 | C22 | semidirect |
| 15. #15690807 | C22 | semidirect |
| 16. #15690721 | C22 | semidirect |
| 20. #124×C97 | C22 | semidirect |
| 32. C2×#11715895 | D4 | semidirect |
| 69. #11715895 | C2×D4 | semidirect |
| 84. C2×C97 | #496 | semidirect |
| 89. C97 | C2×#496 | semidirect |
| 93. C2×#124 | D97 | semidirect |
| 108. #124 | C2×D97 | semidirect |
| 174. C2 | #20261125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C22×#13095496 | 2 |
| C2×#15690807 | 2 |
| #20261125 | 2 |
| C2×#15690721 | 2 |
| C2×#124×C97 | 2 |
| C2×#496 | 97 |