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. C2×#15690897 | C2 | semidirect |
| 3. #20261780 | C2 | direct (N × H) |
| 4. C2×#15690881 | C2 | semidirect |
| 5. C2×#15690875 | C2 | semidirect |
| 6. C2×#15690874 | C2 | semidirect |
| 7. C2×#15690864 | C2 | semidirect |
| 10. #15690898 | C22 | semidirect |
| 12. #15690897 | C22 | semidirect |
| 21. #15690881 | C22 | semidirect |
| 22. #15690875 | C22 | semidirect |
| 23. #15690874 | C22 | semidirect |
| 24. #15690864 | C22 | semidirect |
| 27. #15690831 | C4 | semidirect |
| 29. C2×#13095501 | C4 | semidirect |
| 30. C2×#13095500 | C4 | semidirect |
| 31. C2×#13095496 | C4 | semidirect |
| 33. C2×SD16×C97 | C4 | semidirect |
| 66. #13095501 | C2×C4 | semidirect |
| 67. #13095500 | C2×C4 | semidirect |
| 68. #13095496 | C2×C4 | semidirect |
| 74. SD16×C97 | C2×C4 | semidirect |
| 127. C2×C97 | #444 | semidirect |
| 133. C97 | C2×#444 | semidirect |
| 148. C2×SD16 | #87604 | semidirect |
| 187. SD16 | C2×#87604 | semidirect |
| 263. C2 | #20261780 | 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 |
| C2×#15690897 | 2 |
| #20261780 | 2 |
| C2×#15690881 | 2 |
| C2×#15690875 | 2 |
| C2×#15690874 | 2 |
| C2×#15690864 | 2 |
| C2×#15690831 | 2 |
| C2×#444 | 97 |