Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C2×#14273758 | C2 | direct (N × H) |
| 3. C22×#11745672 | C2 | semidirect |
| 4. C22×#11745671 | C2 | semidirect |
| 5. C22×#11745664 | C2 | semidirect |
| 6. C23×Q8×C59 | C2 | semidirect |
| 13. #14273758 | C22 | direct (N × H) |
| 14. C2×#11745672 | C22 | semidirect |
| 15. C2×#11745671 | C22 | semidirect |
| 16. C2×#11745664 | C22 | semidirect |
| 21. C22×Q8×C59 | C22 | semidirect |
| 30. C2×Q8×C59 | C23 | semidirect |
| 46. #11745672 | C23 | semidirect |
| 47. #11745671 | C23 | semidirect |
| 48. #11745664 | C23 | semidirect |
| 74. C22×C59 | #137 | semidirect |
| 86. C2×C59 | C2×#137 | semidirect |
| 90. C23×Q8 | D59 | semidirect |
| 95. C59 | C22×#137 | semidirect |
| 102. C22×Q8 | C2×D59 | semidirect |
| 123. C2×Q8 | C22×D59 | semidirect |
| 165. C22 | #14273758 | direct (N × H) |
| 175. C2 | C2×#14273758 | direct (N × H) |