Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13095501 | C2 | semidirect |
| 5. #20260975 | C2 | direct (N × H) |
| 6. C2×#15690743 | C2 | semidirect |
| 7. C2×#15690735 | C2 | semidirect |
| 8. C2×#103×C97 | C2 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 25. #15690743 | C22 | semidirect |
| 26. #15690735 | C22 | semidirect |
| 30. #103×C97 | C22 | semidirect |
| 67. C22×D97 | Q16 | semidirect |
| 101. C2×D97 | C2×Q16 | semidirect |
| 110. C2×C97 | #467 | semidirect |
| 116. C97 | C2×#467 | semidirect |
| 124. C2×#103 | D97 | semidirect |
| 146. #103 | C2×D97 | semidirect |
| 227. C2 | #20260975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C22×C8×D97 | 2 |
| C2×#15690790 | 2 |
| C2×#15690786 | 2 |
| #20260975 | 2 |
| C2×#15690743 | 2 |
| C2×#15690735 | 2 |
| C2×#103×C97 | 2 |
| C2×#467 | 97 |