Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20265977 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265193 | C2 | semidirect |
| 5. #20265183 | C2 | semidirect |
| 6. #20265150 | C2 | semidirect |
| 7. #344×C101 | C2 | semidirect |
| 41. C2×Dic202 | D4 | semidirect |
| 50. C2×D404 | D4 | semidirect |
| 69. M16×C101 | D4 | semidirect |
| 71. C2×C8×C101 | D4 | semidirect |
| 143. C101 | #2008 | semidirect |
| 150. #344 | D101 | semidirect |
| 208. M16 | D404 | semidirect |
| 210. C2×C8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692283 | 2 |
| #20265746 | 2 |
| #20265193 | 2 |
| #20265183 | 2 |
| #20265150 | 2 |
| #344×C101 | 2 |
| #2008 | 101 |