Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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×#15692231 | C2 | semidirect |
| 3. #20265096 | C2 | semidirect |
| 4. #20265088 | C2 | semidirect |
| 5. #20265084 | C2 | semidirect |
| 7. #20265050 | C2 | semidirect |
| 8. #20265037 | C2 | semidirect |
| 9. C23×Q8×C101 | C2 | semidirect |
| 34. C2×C22⋊D101 | Q8 | semidirect |
| 55. C2×Q8×C101 | D4 | semidirect |
| 73. C22×D101 | C2×Q8 | semidirect |
| 95. C2×Dic101 | C2×Q8 | semidirect |
| 101. C22×C101 | C22⋊Q8 | semidirect |
| 127. C101 | #2409 | semidirect |
| 128. C23×Q8 | D101 | semidirect |
| 165. C2×Q8 | C22⋊D101 | semidirect |
| 233. C22 | #15692231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692231 | 2 |
| C2×C4×C22⋊D101 | 2 |
| #20265096 | 2 |
| #20265088 | 2 |
| #20265084 | 2 |
| #20265056 | 2 |
| #20265050 | 2 |
| #20265037 | 2 |
| C23×Q8×C101 | 2 |
| #2409 | 101 |