Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692278 | C2 | semidirect |
| 2. C22×C8×D101 | C2 | semidirect |
| 3. #20265690 | C2 | semidirect |
| 4. #20265415 | C2 | semidirect |
| 5. #20265414 | C2 | semidirect |
| 6. #20265413 | C2 | semidirect |
| 7. #20265409 | C2 | semidirect |
| 8. #20265408 | C2 | semidirect |
| 9. #20265214 | C2 | semidirect |
| 10. #20265172 | C2 | semidirect |
| 11. #467×C101 | C2 | semidirect |
| 15. C2×#13108061 | C22 | semidirect |
| 16. C2×D808 | C22 | semidirect |
| 31. #15692189 | C22 | semidirect |
| 32. #15692186 | C22 | semidirect |
| 33. #15692179 | C22 | semidirect |
| 34. #15692177 | C22 | semidirect |
| 35. #15692175 | C22 | semidirect |
| 36. C2×Q16×C101 | C22 | semidirect |
| 39. #107×C101 | C22 | semidirect |
| 40. #103×C101 | C22 | semidirect |
| 64. C8×D101 | D4 | semidirect |
| 118. C22×C101 | #135 | semidirect |
| 129. C2×D101 | #135 | semidirect |
| 146. C101 | #3050 | semidirect |
| 151. #467 | D101 | semidirect |
| 161. C2×Q16 | C2×D101 | semidirect |
| 181. #107 | C2×D101 | semidirect |
| 184. #103 | C2×D101 | semidirect |
| 274. C22 | #15692278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C22×C8×D101 | 2 |
| #20265690 | 2 |
| #20265415 | 2 |
| #20265414 | 2 |
| #20265413 | 2 |
| #20265409 | 2 |
| #20265408 | 2 |
| #20265214 | 2 |
| #20265172 | 2 |
| #467×C101 | 2 |
| #3050 | 101 |