Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D97 | C2 | semidirect |
| 2. C22×#13095500 | C2 | semidirect |
| 3. C22×#13095498 | C2 | semidirect |
| 5. #20260875 | C2 | direct (N × H) |
| 6. C2×#15690733 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C2×#103×C97 | C2 | semidirect |
| 14. C2×Q8×D97 | C22 | semidirect |
| 20. C2×#13095500 | C22 | semidirect |
| 22. C2×#13095498 | C22 | semidirect |
| 27. #15690733 | C22 | semidirect |
| 28. #15690722 | C22 | semidirect |
| 32. #103×C97 | C22 | semidirect |
| 39. C2×Dic194 | D4 | semidirect |
| 65. C2×Q8×C97 | D4 | semidirect |
| 81. C22×D97 | SD16 | semidirect |
| 85. Q8×C97 | C2×D4 | semidirect |
| 109. Dic194 | C2×D4 | semidirect |
| 123. C2×D97 | C2×SD16 | semidirect |
| 131. C2×C97 | #448 | semidirect |
| 138. C97 | C2×#448 | semidirect |
| 145. C2×#103 | D97 | semidirect |
| 169. #103 | C2×D97 | semidirect |
| 184. C2×Q8 | D388 | semidirect |
| 227. Q8 | C2×D388 | semidirect |
| 271. C2 | #20260875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| C22×#13095500 | 2 |
| C22×#13095498 | 2 |
| C2×#15690785 | 2 |
| #20260875 | 2 |
| C2×#15690733 | 2 |
| C2×#15690722 | 2 |
| C2×#103×C97 | 2 |
| C2×#448 | 97 |