Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#15690898 | C2 | semidirect |
| 2. #20261781 | C2 | direct (N × H) |
| 3. C2×#15690880 | C2 | semidirect |
| 4. C2×#15690875 | C2 | semidirect |
| 5. C2×#15690864 | C2 | semidirect |
| 8. #15690898 | C22 | semidirect |
| 14. #15690880 | C22 | semidirect |
| 15. #15690875 | C22 | semidirect |
| 16. #15690864 | C22 | semidirect |
| 18. #15690833 | C4 | semidirect |
| 20. C2×#13095498 | C4 | semidirect |
| 21. C2×D776 | C4 | semidirect |
| 23. C2×Q16×C97 | C4 | semidirect |
| 43. #13095498 | C2×C4 | semidirect |
| 44. D776 | C2×C4 | semidirect |
| 49. Q16×C97 | C2×C4 | semidirect |
| 86. C2×C97 | #444 | semidirect |
| 92. C97 | C2×#444 | semidirect |
| 102. C2×Q16 | #87604 | semidirect |
| 126. Q16 | C2×#87604 | semidirect |
| 181. C2 | #20261781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| #20261781 | 2 |
| C2×#15690880 | 2 |
| C2×#15690875 | 2 |
| C2×#15690864 | 2 |
| C2×#15690833 | 2 |
| C2×#444 | 97 |