Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. #20261022 | C2 | direct (N × H) |
| 3. C2×#15690741 | C2 | semidirect |
| 4. C2×C4⋊#11715895 | C2 | semidirect |
| 6. C2×C4⋊Q8×C97 | C2 | semidirect |
| 14. #15690741 | C22 | semidirect |
| 15. C4⋊#11715895 | C22 | semidirect |
| 19. C4⋊Q8×C97 | C22 | semidirect |
| 26. C2×D388 | Q8 | semidirect |
| 67. D388 | C2×Q8 | semidirect |
| 85. C2×C97 | #476 | semidirect |
| 91. C97 | C2×#476 | semidirect |
| 92. C2×C4⋊Q8 | D97 | semidirect |
| 103. C4⋊Q8 | C2×D97 | semidirect |
| 177. C2 | #20261022 | 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 |
| #20261022 | 2 |
| C2×#15690741 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690730 | 2 |
| C2×C4⋊Q8×C97 | 2 |
| C2×#476 | 97 |