Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20261540 | C2 | semidirect |
| 2. #20261171 | C2 | semidirect |
| 3. C2×#15690751 | C2 | semidirect |
| 4. #20260547 | C2 | semidirect |
| 5. #20260541 | C2 | semidirect |
| 6. #20260519 | C2 | semidirect |
| 7. #472×C97 | C2 | semidirect |
| 18. #15690750 | C22 | semidirect |
| 19. C2×#13095486 | C22 | semidirect |
| 21. C2×D8×C97 | C22 | semidirect |
| 23. #108×C97 | C22 | semidirect |
| 94. C97 | #2192 | semidirect |
| 98. #472 | D97 | semidirect |
| 110. C2×D8 | C2×D97 | semidirect |
| 117. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261540 | 2 |
| #20261171 | 2 |
| C2×#15690751 | 2 |
| #20260547 | 2 |
| #20260541 | 2 |
| #20260519 | 2 |
| #472×C97 | 2 |
| #2192 | 97 |