Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. M16×#87938 | C2 | semidirect |
| 4. #20266113 | C2 | semidirect |
| 5. #20266049 | C2 | semidirect |
| 6. #20266048 | C2 | semidirect |
| 9. Q8×#87938 | C4 | semidirect |
| 11. D4×#87938 | C4 | semidirect |
| 17. #15692320 | C4 | semidirect |
| 18. #15692319 | C4 | semidirect |
| 25. #15692183 | C4 | semidirect |
| 26. #15692182 | C4 | semidirect |
| 27. #15692181 | C4 | semidirect |
| 28. #104×C101 | C4 | semidirect |
| 32. #13108084 | C2×C4 | semidirect |
| 43. C4×#87938 | C2×C4 | semidirect |
| 57. #13108058 | C2×C4 | semidirect |
| 61. C4×Dic101 | C2×C4 | semidirect |
| 63. M16×C101 | C2×C4 | semidirect |
| 64. C42×C101 | C2×C4 | semidirect |
| 127. C101 | #1759 | semidirect |
| 152. #104 | #87938 | semidirect |
| 175. M16 | C2×#87938 | semidirect |
| 191. C42 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#87938 | 2 |
| D101⋊#104 | 2 |
| M16×#87938 | 2 |
| #20266113 | 2 |
| #20266049 | 2 |
| #20266048 | 2 |
| #104×D101 | 2 |
| #1759 | 101 |