Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#495 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #495 | D59 |
| hypocenter | C59 | #3273 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #495 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273754 | C2 | semidirect |
| 2. #16838045 | C2 | semidirect |
| 3. #16837645 | C2 | semidirect |
| 4. #16837614 | C2 | semidirect |
| 5. #16837563 | C2 | semidirect |
| 6. #16837534 | C2 | semidirect |
| 7. C4×D472 | C2 | semidirect |
| 8. #16837481 | C2 | semidirect |
| 9. C59×#495 | C2 | semidirect |
| 11. C2×D4×D59 | C22 | semidirect |
| 13. C2×#11745671 | C22 | semidirect |
| 16. C2×#11745659 | C22 | semidirect |
| 18. #14273703 | C22 | semidirect |
| 23. C4×D236 | C22 | semidirect |
| 25. #14273661 | C22 | semidirect |
| 26. C4⋊(C59⋊C8) | C22 | semidirect |
| 27. #14273651 | C22 | semidirect |
| 28. #14273649 | C22 | semidirect |
| 29. #14273648 | C22 | semidirect |
| 30. (C2×D59)⋊C8 | C22 | semidirect |
| 31. C2×Q16×C59 | C22 | semidirect |
| 32. C2×SD16×C59 | C22 | semidirect |
| 34. #124×C59 | C22 | semidirect |
| 35. C4×C8×C59 | C22 | semidirect |
| 69. D472 | D4 | semidirect |
| 127. #495 | D59 | semidirect |
| 134. C59 | #3273 | semidirect |
| 138. C2×Q16 | C2×D59 | semidirect |
| 140. C2×SD16 | C2×D59 | semidirect |
| 145. #124 | C2×D59 | semidirect |
| 160. C4×C8 | C2×D59 | semidirect |