Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 438 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 |
|---|---|---|
| 1. C2×D4×#87604 | C2 | semidirect |
| 2. C2×#15690872 | C2 | semidirect |
| 3. C2×#15690872 | C2 | semidirect |
| 4. #20261687 | C2 | semidirect |
| 5. #20261609 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 22. C2×D776 | C4 | semidirect |
| 23. C2×#13095496 | C4 | semidirect |
| 24. C2×#13095496 | C4 | semidirect |
| 28. C2×D8×C97 | C4 | semidirect |
| 51. C2×D388 | C2×C4 | semidirect |
| 66. C2×#11715895 | C2×C4 | semidirect |
| 70. C2×D4×C97 | C2×C4 | semidirect |
| 72. C2×C8×C97 | C2×C4 | semidirect |
| 102. C2×#87604 | D8 | semidirect |
| 106. D4×C97 | C22⋊C4 | semidirect |
| 116. D388 | C22⋊C4 | semidirect |
| 171. C97 | #1879 | semidirect |
| 187. C2×D8 | #87604 | semidirect |
| 215. C2×D4 | C2×#87604 | semidirect |
| 234. C2×C8 | C2×#87604 | semidirect |
| 272. D4 | C22⋊#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×#15690872 | 2 |
| #20261687 | 2 |
| #20261609 | 2 |
| #20261600 | 2 |
| C2×D8×D97 | 2 |
| #1879 | 97 |