Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
719 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 719 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22⋊C4×AGL(1,𝔽9) | C2 | semidirect |
| 5. #11770846 | C2 | semidirect |
| 6. C23×AGL(1,𝔽9) | C4 | semidirect |
| 9. C2×C22⋊AGL(1,𝔽9) | C4 | semidirect |
| 14. C2×C4⋊AGL(1,𝔽9) | C4 | semidirect |
| 16. C2×C4×AGL(1,𝔽9) | C4 | semidirect |
| 19. #10593272 | C4 | semidirect |
| 21. #10593260 | C4 | semidirect |
| 55. #63786 | C8 | semidirect |
| 57. #63774 | C8 | semidirect |
| 58. C32×#99 | C8 | semidirect |
| 59. #63661 | C8 | semidirect |
| 60. #63633 | C8 | semidirect |
| 105. C22⋊#157 | C2×C8 | semidirect |
| 111. C32×C22⋊C4 | C2×C8 | semidirect |
| 112. #3757 | C2×C8 | semidirect |
| 124. C23×C32 | C4×C8 | semidirect |
| 132. C22×C3⋊D3 | C4×C8 | semidirect |
| 161. AGL(1,𝔽9) | #99 | direct (N × H) |
| 164. C2×C32×C4 | C4×C8 | semidirect |
| 168. C2×C3⋊Dic3 | C4×C8 | semidirect |
| 263. #99 | AGL(1,𝔽9) | direct (N × H) |
| 352. C22⋊C4 | C2×AGL(1,𝔽9) | semidirect |
| 380. C32 | C8×#99 | semidirect |
| 392. C23 | C4×AGL(1,𝔽9) | semidirect |
| 424. C2×C4 | C4×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×AGL(1,𝔽9) | 2 |
| #99×#157 | 2 |
| C22⋊C4×AGL(1,𝔽9) | 2 |
| #11773799 | 2 |
| #11770846 | 2 |
| C8×#99 | 9 |