Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. C4×#13108075 | C2 | semidirect |
| 3. #20265290 | C2 | semidirect |
| 4. #20265288 | C2 | semidirect |
| 5. #20265284 | C2 | semidirect |
| 6. #20265280 | C2 | semidirect |
| 7. #20265275 | C2 | semidirect |
| 8. #20265212 | C2 | semidirect |
| 9. #20265172 | C2 | semidirect |
| 10. #97×D101 | C2 | semidirect |
| 11. #441×C101 | C2 | semidirect |
| 13. #15692278 | C4 | semidirect |
| 41. #13108075 | C2×C4 | semidirect |
| 49. #13108061 | C2×C4 | semidirect |
| 50. D808 | C2×C4 | semidirect |
| 54. C8×D101 | C2×C4 | semidirect |
| 65. Q16×C101 | C2×C4 | semidirect |
| 115. C101 | #2943 | semidirect |
| 121. #441 | D101 | semidirect |
| 165. Q16 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C4×#13108075 | 2 |
| #20265290 | 2 |
| #20265288 | 2 |
| #20265284 | 2 |
| #20265280 | 2 |
| #20265275 | 2 |
| #20265212 | 2 |
| #20265172 | 2 |
| #97×D101 | 2 |
| #441×C101 | 2 |
| #2943 | 101 |