Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#3633 |
| commutator, socle | C2×C17 | C23×C8 |
| Fitting | #41×C17 | C8 |
| prime radical | #41×D17 | C4 |
| cosocle | C2×#595 | C24 |
| hypercenter | #41 | #3633 |
| hypocenter | C17 | #2988 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#3633 | C2 | semidirect |
| 2. D4×#3633 | C2 | semidirect |
| 3. #11763922 | C2 | semidirect |
| 4. C2×C4⋊#3633 | C2 | semidirect |
| 24. #41×C17 | C8 | semidirect |
| 25. #63256 | C8 | semidirect |
| 27. #63254 | C8 | semidirect |
| 29. #63252 | C8 | semidirect |
| 48. Q8×C17 | C2×C8 | semidirect |
| 49. D4×C17 | C2×C8 | semidirect |
| 50. C2×C4×C17 | C2×C8 | semidirect |
| 51. C22⋊D17 | C2×C8 | semidirect |
| 52. C2×Dic17 | C2×C8 | semidirect |
| 53. D68 | C2×C8 | semidirect |
| 54. C4×D17 | C2×C8 | semidirect |
| 55. C4×D17 | C2×C8 | semidirect |
| 58. Dic34 | C2×C8 | semidirect |
| 97. C17 | #2988 | semidirect |
| 101. #41 | #3633 | semidirect |
| 119. Q8 | C2×#3633 | semidirect |
| 122. D4 | C2×#3633 | semidirect |
| 135. C2×C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3633 | 2 |
| D4×#3633 | 2 |
| #11763922 | 2 |
| C2×C4⋊#3633 | 2 |
| #41×#595 | 2 |
| #2988 | 17 |