Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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×C4 | C23×D17 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting, prime radical | C17×#525 | C2 |
| cosocle | C2×C4×C17 | C24 |
| hypercenter | #525 | D17 |
| hypocenter | C17 | #2978 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11762887 | C2 | semidirect |
| 2. #11762881 | C2 | semidirect |
| 3. #11762870 | C2 | semidirect |
| 4. #11762776 | C2 | semidirect |
| 5. #11762773 | C2 | semidirect |
| 16. C2×#63223 | C22 | semidirect |
| 17. C22×#3622 | C22 | semidirect |
| 21. C22⋊#3622 | C22 | semidirect |
| 22. C4⋊#3622 | C22 | semidirect |
| 23. #10587474 | C22 | semidirect |
| 24. C4×#3622 | C22 | semidirect |
| 114. C17 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762887 | 2 |
| #11762881 | 2 |
| #11762870 | 2 |
| #11762776 | 2 |
| #11762773 | 2 |
| C17×#525 | 2 |
| #2978 | 17 |