Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×#15690873 | C2 | semidirect |
| 4. (C2×#87604)⋊Q8 | C2 | semidirect |
| 5. #20261609 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 22. C2×#13095500 | C4 | semidirect |
| 23. C2×#13095499 | C4 | semidirect |
| 24. C2×#13095498 | C4 | semidirect |
| 28. C2×SD16×C97 | C4 | semidirect |
| 48. C2×Dic194 | C2×C4 | semidirect |
| 64. C2×#11715895 | C2×C4 | semidirect |
| 67. C2×Q8×C97 | C2×C4 | semidirect |
| 70. C2×C8×C97 | C2×C4 | semidirect |
| 92. C2×#87604 | SD16 | semidirect |
| 155. C97 | #1877 | semidirect |
| 171. C2×SD16 | #87604 | semidirect |
| 191. C2×Q8 | C2×#87604 | semidirect |
| 218. C2×C8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#87604 | 2 |
| C2×#15690873 | 2 |
| C2×#15690872 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261609 | 2 |
| #20261600 | 2 |
| C2×SD16×D97 | 2 |
| #1877 | 97 |