Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15692277 | C2 | semidirect |
| 2. C2×#15692275 | C2 | semidirect |
| 3. #20265723 | C2 | semidirect |
| 4. #20265562 | C2 | semidirect |
| 5. #20265560 | C2 | semidirect |
| 6. #20265558 | C2 | semidirect |
| 7. #20265555 | C2 | semidirect |
| 8. #20265552 | C2 | semidirect |
| 9. #20265548 | C2 | semidirect |
| 10. C2×C8×Dic101 | C2 | semidirect |
| 11. C2×#135×C101 | C2 | semidirect |
| 55. C2×#11717579 | D4 | semidirect |
| 74. C2×C8×C101 | D4 | semidirect |
| 119. Dic101 | #135 | semidirect |
| 126. C101 | #3147 | semidirect |
| 129. C2×#135 | D101 | semidirect |
| 194. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C2×#15692275 | 2 |
| #20265723 | 2 |
| #20265562 | 2 |
| #20265560 | 2 |
| #20265558 | 2 |
| #20265555 | 2 |
| #20265552 | 2 |
| #20265548 | 2 |
| C2×C8×Dic101 | 2 |
| C2×#135×C101 | 2 |
| #3147 | 101 |