Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#15690864 | C2 | semidirect |
| 3. C2×C8×#87604 | C2 | semidirect |
| 5. #20261600 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 8. C2×#13095521 | C4 | semidirect |
| 11. C2×#13095520 | C4 | semidirect |
| 23. C22⋊#11715895 | C4 | semidirect |
| 24. #15690722 | C4 | semidirect |
| 25. #15690722 | C4 | semidirect |
| 26. C22⋊C8×C97 | C4 | semidirect |
| 73. C2×#87604 | M16 | semidirect |
| 93. #11715897 | C22⋊C4 | semidirect |
| 127. C97 | #1753 | semidirect |
| 150. C22⋊C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C2×#15690864 | 2 |
| C2×C8×#87604 | 2 |
| C4×C22⋊#87604 | 2 |
| #20261600 | 2 |
| C22⋊C8×D97 | 2 |
| #1753 | 97 |