Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #20261032 | C2 | direct (N × H) |
| 3. C2×#15690743 | C2 | semidirect |
| 4. C2×#15690741 | C2 | semidirect |
| 5. C2×C4⋊#11715895 | C2 | semidirect |
| 8. C2×#125×C97 | C2 | semidirect |
| 17. #15690743 | C22 | semidirect |
| 18. #15690741 | C22 | semidirect |
| 19. C4⋊#11715895 | C22 | semidirect |
| 23. #125×C97 | C22 | semidirect |
| 98. C2×C97 | #478 | semidirect |
| 104. C97 | C2×#478 | semidirect |
| 105. C2×#125 | D97 | semidirect |
| 118. #125 | C2×D97 | semidirect |
| 203. C2 | #20261032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| #20261032 | 2 |
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690730 | 2 |
| C2×#125×C97 | 2 |
| C2×#478 | 97 |