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×#13095500 | C2 | semidirect |
| 2. C22×#13095499 | C2 | semidirect |
| 3. C22×#13095496 | C2 | semidirect |
| 4. C2×#15690806 | C2 | semidirect |
| 5. C2×#15690797 | C2 | semidirect |
| 6. #20261123 | C2 | direct (N × H) |
| 7. C2×#15690720 | C2 | semidirect |
| 8. C22×D8×C97 | C2 | semidirect |
| 13. C2×#13095500 | C22 | semidirect |
| 15. C2×#13095499 | C22 | semidirect |
| 17. C2×#13095496 | C22 | semidirect |
| 20. #15690806 | C22 | semidirect |
| 22. #15690797 | C22 | semidirect |
| 25. #15690720 | C22 | semidirect |
| 29. C2×D8×C97 | C22 | semidirect |
| 47. C2×#11715895 | D4 | semidirect |
| 64. C2×C8×C97 | D4 | semidirect |
| 97. C8×C97 | C2×D4 | semidirect |
| 98. #11715895 | C2×D4 | semidirect |
| 118. C2×C97 | #496 | semidirect |
| 123. C97 | C2×#496 | semidirect |
| 127. C22×D8 | D97 | semidirect |
| 144. C2×D8 | C2×D97 | semidirect |
| 184. C2×C8 | C22⋊D97 | semidirect |
| 221. C8 | C2×C22⋊D97 | semidirect |
| 242. C2 | #20261123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C22×#13095499 | 2 |
| C22×#13095496 | 2 |
| C2×#15690806 | 2 |
| C2×#15690797 | 2 |
| #20261123 | 2 |
| C2×#15690720 | 2 |
| C22×D8×C97 | 2 |
| C2×#496 | 97 |