Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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. C23×H(5,𝔽2) | C2 | semidirect |
| 2. #10625160 | C2 | semidirect |
| 3. #10625121 | C2 | semidirect |
| 4. #10625120 | C2 | semidirect |
| 5. #10625119 | C2 | semidirect |
| 6. #10625103 | C2 | semidirect |
| 7. C2×#67272 | C2 | semidirect |
| 10. #41×C23 | C22 | semidirect |
| 12. C2×D4×C23 | C22 | semidirect |
| 15. #67288 | C22 | semidirect |
| 16. C2×D92 | C22 | semidirect |
| 17. #67275 | C22 | semidirect |
| 18. #67274 | C22 | semidirect |
| 19. #67273 | C22 | semidirect |
| 20. #67272 | C22 | semidirect |
| 21. #67272 | C22 | semidirect |
| 22. #67267 | C22 | semidirect |
| 23. C2×C23⋊C8 | C22 | semidirect |
| 56. H(5,𝔽2) | D23 | semidirect |
| 62. C23 | #576 | semidirect |
| 67. #41 | C2×D23 | semidirect |
| 71. C2×D4 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×H(5,𝔽2) | 2 |
| #10625160 | 2 |
| #10625121 | 2 |
| #10625120 | 2 |
| #10625119 | 2 |
| #10625103 | 2 |
| C2×#67272 | 2 |
| #576 | 23 |