Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 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. C2×#15690809 | C2 | semidirect |
| 3. #20261014 | C2 | direct (N × H) |
| 4. C2×#15690743 | C2 | semidirect |
| 5. C2×#15690739 | C2 | semidirect |
| 8. C2×#107×C97 | C2 | semidirect |
| 14. #15690809 | C22 | semidirect |
| 21. #15690743 | C22 | semidirect |
| 22. #15690739 | C22 | semidirect |
| 28. #107×C97 | C22 | semidirect |
| 34. C2×D388 | Q8 | semidirect |
| 79. D388 | C2×Q8 | semidirect |
| 100. C2×C97 | #474 | semidirect |
| 106. C97 | C2×#474 | semidirect |
| 111. C2×#107 | D97 | semidirect |
| 131. #107 | C2×D97 | semidirect |
| 207. C2 | #20261014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690809 | 2 |
| C2×#15690772 | 2 |
| #20261014 | 2 |
| C2×#15690743 | 2 |
| C2×#15690739 | 2 |
| C2×#15690732 | 2 |
| C2×#15690730 | 2 |
| C2×#107×C97 | 2 |
| C2×#474 | 97 |