Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 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×Q8×#1181 | C2 | semidirect |
| 2. (C2×#1181)⋊Q8 | C2 | semidirect |
| 6. C22×Q8×C29 | C4 | semidirect |
| 8. C2×Q8×D29 | C4 | semidirect |
| 9. C2×Q8×D29 | C4 | semidirect |
| 13. C22×Dic58 | C4 | semidirect |
| 43. C22⋊#1181 | Q8 | direct (N × H) |
| 58. C2×#1181 | C2×Q8 | semidirect |
| 60. Q8×C29 | C22⋊C4 | semidirect |
| 73. Dic58 | C22⋊C4 | semidirect |
| 77. C22×C29 | C4×Q8 | semidirect |
| 83. C2×D29 | C4×Q8 | semidirect |
| 112. C22×Q8 | #1181 | semidirect |
| 121. C29 | Q8×C22⋊C4 | semidirect |
| 158. Q8 | C22⋊#1181 | direct (N × H) |
| 186. C22 | Q8×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| (C2×#1181)⋊Q8 | 2 |
| #14272105 | 2 |
| C4×C22⋊#1181 | 2 |
| C22×Q8×D29 | 2 |
| Q8×C22⋊C4 | 29 |